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

@@ -4,9 +4,9 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker, Johan Commelin
 -/
 import Algebra.CharZero.Infinite
-import Data.Polynomial.AlgebraMap
-import Data.Polynomial.Degree.Lemmas
-import Data.Polynomial.Div
+import Algebra.Polynomial.AlgebraMap
+import Algebra.Polynomial.Degree.Lemmas
+import Algebra.Polynomial.Div
 import RingTheory.Localization.FractionRing
 import Algebra.Polynomial.BigOperators
 

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

@@ -556,7 +556,7 @@ theorem rootMultiplicity_X_sub_C_pow (a : R) (n : ℕ) : rootMultiplicity a ((X
   · refine' root_multiplicity_eq_zero _
     simp only [eval_one, is_root.def, not_false_iff, one_ne_zero, pow_zero]
   have hzero := pow_ne_zero n.succ (X_sub_C_ne_zero a)
-  rw [pow_succ (X - C a) n] at hzero ⊢
+  rw [pow_succ' (X - C a) n] at hzero ⊢
   simp only [root_multiplicity_mul hzero, root_multiplicity_X_sub_C_self, hn, Nat.one_add]
 #align polynomial.root_multiplicity_X_sub_C_pow Polynomial.rootMultiplicity_X_sub_C_pow
 -/
@@ -854,7 +854,7 @@ theorem roots_pow (p : R[X]) (n : ℕ) : (p ^ n).roots = n • p.roots :=
   · rcases eq_or_ne p 0 with (rfl | hp)
     · rw [zero_pow n.succ_pos, roots_zero, smul_zero]
     ·
-      rw [pow_succ', roots_mul (mul_ne_zero (pow_ne_zero _ hp) hp), ihn, Nat.succ_eq_add_one,
+      rw [pow_succ, roots_mul (mul_ne_zero (pow_ne_zero _ hp) hp), ihn, Nat.succ_eq_add_one,
         add_smul, one_smul]
 #align polynomial.roots_pow Polynomial.roots_pow
 -/

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

@@ -196,7 +196,7 @@ theorem degree_le_mul_left (p : R[X]) (hq : q ≠ 0) : degree p ≤ degree (p *
 #print Polynomial.natDegree_le_of_dvd /-
 theorem natDegree_le_of_dvd {p q : R[X]} (h1 : p ∣ q) (h2 : q ≠ 0) : p.natDegree ≤ q.natDegree :=
   by
-  rcases h1 with ⟨q, rfl⟩; rw [mul_ne_zero_iff] at h2 
+  rcases h1 with ⟨q, rfl⟩; rw [mul_ne_zero_iff] at h2
   rw [nat_degree_mul h2.1 h2.2]; exact Nat.le_add_right _ _
 #align polynomial.nat_degree_le_of_dvd Polynomial.natDegree_le_of_dvd
 -/
@@ -204,7 +204,7 @@ theorem natDegree_le_of_dvd {p q : R[X]} (h1 : p ∣ q) (h2 : q ≠ 0) : p.natDe
 #print Polynomial.degree_le_of_dvd /-
 theorem degree_le_of_dvd {p q : R[X]} (h1 : p ∣ q) (h2 : q ≠ 0) : degree p ≤ degree q :=
   by
-  rcases h1 with ⟨q, rfl⟩; rw [mul_ne_zero_iff] at h2 
+  rcases h1 with ⟨q, rfl⟩; rw [mul_ne_zero_iff] at h2
   exact degree_le_mul_left p h2.2
 #align polynomial.degree_le_of_dvd Polynomial.degree_le_of_dvd
 -/
@@ -259,7 +259,7 @@ theorem natDegree_eq_zero_of_isUnit (h : IsUnit p) : natDegree p = 0 :=
   nontriviality R
   obtain ⟨q, hq⟩ := h.exists_right_inv
   have := nat_degree_mul (left_ne_zero_of_mul_eq_one hq) (right_ne_zero_of_mul_eq_one hq)
-  rw [hq, nat_degree_one, eq_comm, add_eq_zero_iff] at this 
+  rw [hq, nat_degree_one, eq_comm, add_eq_zero_iff] at this
   exact this.1
 #align polynomial.nat_degree_eq_zero_of_is_unit Polynomial.natDegree_eq_zero_of_isUnit
 -/
@@ -367,7 +367,7 @@ theorem Monic.irreducible_iff_natDegree' (hp : p.Monic) :
   constructor <;> intro h f g hf hg he <;> subst he
   · rw [hf.nat_degree_mul hg, add_le_add_iff_right]
     exact fun ha => (h f g hf hg rfl).elim (ha.1.trans_le ha.2).ne' ha.1.ne'
-  · simp_rw [hf.nat_degree_mul hg, pos_iff_ne_zero] at h 
+  · simp_rw [hf.nat_degree_mul hg, pos_iff_ne_zero] at h
     contrapose! h
     obtain hl | hl := le_total f.nat_degree g.nat_degree
     · exact ⟨g, f, hg, hf, mul_comm g f, h.1, add_le_add_left hl _⟩
@@ -384,7 +384,7 @@ theorem Monic.not_irreducible_iff_exists_add_mul_eq_coeff (hm : p.Monic) (hnd :
   rw [hm.irreducible_iff_nat_degree', and_iff_right, hnd]
   push_neg; constructor
   · rintro ⟨a, b, ha, hb, rfl, hdb | ⟨⟨⟩⟩⟩
-    have hda := hnd; rw [ha.nat_degree_mul hb, hdb] at hda 
+    have hda := hnd; rw [ha.nat_degree_mul hb, hdb] at hda
     use a.coeff 0, b.coeff 0, mul_coeff_zero a b
     simpa only [next_coeff, hnd, add_right_cancel hda, hdb] using ha.next_coeff_mul hb
   · rintro ⟨c₁, c₂, hmul, hadd⟩
@@ -510,10 +510,10 @@ theorem Monic.irreducible_of_degree_eq_one (hp1 : degree p = 1) (hm : Monic p) :
 theorem eq_of_monic_of_associated (hp : p.Monic) (hq : q.Monic) (hpq : Associated p q) : p = q :=
   by
   obtain ⟨u, hu⟩ := hpq
-  unfold monic at hp hq 
-  rw [eq_C_of_degree_le_zero (degree_coe_units _).le] at hu 
-  rw [← hu, leading_coeff_mul, hp, one_mul, leading_coeff_C] at hq 
-  rwa [hq, C_1, mul_one] at hu 
+  unfold monic at hp hq
+  rw [eq_C_of_degree_le_zero (degree_coe_units _).le] at hu
+  rw [← hu, leading_coeff_mul, hp, one_mul, leading_coeff_C] at hq
+  rwa [hq, C_1, mul_one] at hu
   all_goals infer_instance
 #align polynomial.eq_of_monic_of_associated Polynomial.eq_of_monic_of_associated
 -/
@@ -571,15 +571,14 @@ theorem exists_multiset_roots [DecidableEq R] :
       let ⟨x, hx⟩ := h
       have hpd : 0 < degree p := degree_pos_of_root hp hx
       have hd0 : p /ₘ (X - C x) ≠ 0 := fun h => by
-        rw [← mul_div_by_monic_eq_iff_is_root.2 hx, h, MulZeroClass.mul_zero] at hp  <;>
-          exact hp rfl
+        rw [← mul_div_by_monic_eq_iff_is_root.2 hx, h, MulZeroClass.mul_zero] at hp <;> exact hp rfl
       have wf : degree (p /ₘ _) < degree p :=
         degree_div_by_monic_lt _ (monic_X_sub_C x) hp ((degree_X_sub_C x).symm ▸ by decide)
       let ⟨t, htd, htr⟩ := @exists_multiset_roots (p /ₘ (X - C x)) hd0
       have hdeg : degree (X - C x) ≤ degree p :=
         by
         rw [degree_X_sub_C, degree_eq_nat_degree hp]
-        rw [degree_eq_nat_degree hp] at hpd 
+        rw [degree_eq_nat_degree hp] at hpd
         exact WithBot.coe_le_coe.2 (WithBot.coe_lt_coe.1 hpd)
       have hdiv0 : p /ₘ (X - C x) ≠ 0 :=
         mt (div_by_monic_eq_zero_iff (monic_X_sub_C x)).1 <| not_lt.2 hdeg
@@ -825,7 +824,7 @@ theorem roots_list_prod (L : List R[X]) :
     (0 : R[X]) ∉ L → L.Prod.roots = (L : Multiset R[X]).bind roots :=
   List.recOn L (fun _ => roots_one) fun hd tl ih H =>
     by
-    rw [List.mem_cons, not_or] at H 
+    rw [List.mem_cons, not_or] at H
     rw [List.prod_cons, roots_mul (mul_ne_zero (Ne.symm H.1) <| List.prod_ne_zero H.2), ←
       Multiset.cons_coe, Multiset.cons_bind, ih H.2]
 #align polynomial.roots_list_prod Polynomial.roots_list_prod
@@ -833,7 +832,7 @@ theorem roots_list_prod (L : List R[X]) :
 
 #print Polynomial.roots_multiset_prod /-
 theorem roots_multiset_prod (m : Multiset R[X]) : (0 : R[X]) ∉ m → m.Prod.roots = m.bind roots := by
-  rcases m with ⟨L⟩; simpa only [Multiset.coe_prod, quot_mk_to_coe''] using roots_list_prod L
+  rcases m with ⟨L⟩; simpa only [Multiset.prod_coe, quot_mk_to_coe''] using roots_list_prod L
 #align polynomial.roots_multiset_prod Polynomial.roots_multiset_prod
 -/
 
@@ -1002,7 +1001,7 @@ theorem Monic.comp (hp : p.Monic) (hq : q.Monic) (h : q.natDegree ≠ 0) : (p.co
 theorem Monic.comp_X_add_C (hp : p.Monic) (r : R) : (p.comp (X + C r)).Monic :=
   by
   refine' hp.comp (monic_X_add_C _) fun ha => _
-  rw [nat_degree_X_add_C] at ha 
+  rw [nat_degree_X_add_C] at ha
   exact one_ne_zero ha
 #align polynomial.monic.comp_X_add_C Polynomial.Monic.comp_X_add_C
 -/
@@ -1035,9 +1034,9 @@ theorem comp_eq_zero_iff : p.comp q = 0 ↔ p = 0 ∨ p.eval (q.coeff 0) = 0 ∧
       rw [← mul_eq_zero, ← nat_degree_comp, h, nat_degree_zero]
     replace key := Or.imp eq_C_of_nat_degree_eq_zero eq_C_of_nat_degree_eq_zero key
     cases key
-    · rw [key, C_comp] at h 
+    · rw [key, C_comp] at h
       exact Or.inl (key.trans h)
-    · rw [key, comp_C, C_eq_zero] at h 
+    · rw [key, comp_C, C_eq_zero] at h
       exact Or.inr ⟨h, key⟩
   ·
     exact fun h =>
@@ -1167,7 +1166,7 @@ theorem rootSet_maps_to' {p : T[X]} {S S'} [CommRing S] [IsDomain S] [Algebra T
 
 #print Polynomial.ne_zero_of_mem_rootSet /-
 theorem ne_zero_of_mem_rootSet {p : T[X]} [CommRing S] [IsDomain S] [Algebra T S] {a : S}
-    (h : a ∈ p.rootSet S) : p ≠ 0 := fun hf => by rwa [hf, root_set_zero] at h 
+    (h : a ∈ p.rootSet S) : p ≠ 0 := fun hf => by rwa [hf, root_set_zero] at h
 #align polynomial.ne_zero_of_mem_root_set Polynomial.ne_zero_of_mem_rootSet
 -/
 
@@ -1218,7 +1217,7 @@ theorem degree_eq_one_of_irreducible_of_root (hi : Irreducible p) {x : R} (hx :
     (fun h => by
       have h₁ : degree (X - C x) = 1 := degree_X_sub_C x
       have h₂ : degree (X - C x) = 0 := degree_eq_zero_of_isUnit h
-      rw [h₁] at h₂  <;> exact absurd h₂ (by decide))
+      rw [h₁] at h₂ <;> exact absurd h₂ (by decide))
     fun hgu => by rw [hg, degree_mul, degree_X_sub_C, degree_eq_zero_of_is_unit hgu, add_zero]
 #align polynomial.degree_eq_one_of_irreducible_of_root Polynomial.degree_eq_one_of_irreducible_of_root
 -/
@@ -1258,9 +1257,9 @@ theorem eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le {R} [CommRing R] {p
   obtain ⟨r, hr⟩ := hdiv
   obtain rfl | hq := eq_or_ne q 0; · simp
   have rzero : r ≠ 0 := fun h => by simpa [h, hq] using hr
-  rw [hr, nat_degree_mul'] at hdeg ; swap
+  rw [hr, nat_degree_mul'] at hdeg; swap
   · rw [hp.leading_coeff, one_mul, leading_coeff_ne_zero]; exact rzero
-  rw [mul_comm, @eq_C_of_nat_degree_eq_zero _ _ r] at hr 
+  rw [mul_comm, @eq_C_of_nat_degree_eq_zero _ _ r] at hr
   · convert hr; convert leading_coeff_C _ using 1; rw [hr, leading_coeff_mul_monic hp]
   · exact (add_right_inj _).1 (le_antisymm hdeg <| Nat.le.intro rfl)
 #align polynomial.eq_leading_coeff_mul_of_monic_of_dvd_of_nat_degree_le Polynomial.eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le
@@ -1344,12 +1343,12 @@ theorem exists_prod_multiset_X_sub_C_mul (p : R[X]) :
   obtain ⟨q, he⟩ := p.prod_multiset_X_sub_C_dvd
   use q, he.symm
   obtain rfl | hq := eq_or_ne q 0
-  · rw [MulZeroClass.mul_zero] at he ; subst he; simp
+  · rw [MulZeroClass.mul_zero] at he; subst he; simp
   constructor
   · conv_rhs => rw [he]
     rw [monic_prod_multiset_X_sub_C.nat_degree_mul' hq, nat_degree_multiset_prod_X_sub_C_eq_card]
   · replace he := congr_arg roots he.symm
-    rw [roots_mul, roots_multiset_prod_X_sub_C] at he 
+    rw [roots_mul, roots_multiset_prod_X_sub_C] at he
     exacts [add_right_eq_self.1 he, mul_ne_zero monic_prod_multiset_X_sub_C.ne_zero hq]
 #align polynomial.exists_prod_multiset_X_sub_C_mul Polynomial.exists_prod_multiset_X_sub_C_mul
 -/
@@ -1482,7 +1481,7 @@ theorem isUnit_of_isUnit_leadingCoeff_of_isUnit_map {f : R[X]} (hf : IsUnit f.le
     (H : IsUnit (map φ f)) : IsUnit f :=
   by
   have dz := degree_eq_zero_of_is_unit H
-  rw [degree_map_eq_of_leading_coeff_ne_zero] at dz 
+  rw [degree_map_eq_of_leading_coeff_ne_zero] at dz
   · rw [eq_C_of_degree_eq_zero dz]
     refine' IsUnit.map C _
     convert hf
@@ -1491,7 +1490,7 @@ theorem isUnit_of_isUnit_leadingCoeff_of_isUnit_map {f : R[X]} (hf : IsUnit f.le
     simpa using H
   · intro h
     have u : IsUnit (φ f.leading_coeff) := IsUnit.map φ hf
-    rw [h] at u 
+    rw [h] at u
     simpa using u
 #align polynomial.is_unit_of_is_unit_leading_coeff_of_is_unit_map Polynomial.isUnit_of_isUnit_leadingCoeff_of_isUnit_map
 -/
@@ -1513,9 +1512,9 @@ theorem Monic.irreducible_of_irreducible_map (f : R[X]) (h_mon : Monic f)
     (h_irr : Irreducible (map φ f)) : Irreducible f :=
   by
   refine' ⟨h_irr.not_unit ∘ IsUnit.map (map_ring_hom φ), fun a b h => _⟩
-  dsimp [monic] at h_mon 
+  dsimp [monic] at h_mon
   have q := (leading_coeff_mul a b).symm
-  rw [← h, h_mon] at q 
+  rw [← h, h_mon] at q
   refine'
         (h_irr.is_unit_or_is_unit <| (congr_arg (map φ) h).trans (Polynomial.map_mul φ)).imp _ _ <;>
       apply is_unit_of_is_unit_leading_coeff_of_is_unit_map <;>

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

@@ -172,12 +172,24 @@ theorem trailingDegree_mul : (p * q).trailingDegree = p.trailingDegree + q.trail
 
 #print Polynomial.natDegree_pow /-
 @[simp]
-theorem natDegree_pow (p : R[X]) (n : ℕ) : natDegree (p ^ n) = n * natDegree p := by classical
+theorem natDegree_pow (p : R[X]) (n : ℕ) : natDegree (p ^ n) = n * natDegree p := by
+  classical exact
+    if hp0 : p = 0 then
+      if hn0 : n = 0 then by simp [hp0, hn0]
+      else by rw [hp0, zero_pow (Nat.pos_of_ne_zero hn0)] <;> simp
+    else
+      nat_degree_pow'
+        (by rw [← leading_coeff_pow, Ne.def, leading_coeff_eq_zero] <;> exact pow_ne_zero _ hp0)
 #align polynomial.nat_degree_pow Polynomial.natDegree_pow
 -/
 
 #print Polynomial.degree_le_mul_left /-
-theorem degree_le_mul_left (p : R[X]) (hq : q ≠ 0) : degree p ≤ degree (p * q) := by classical
+theorem degree_le_mul_left (p : R[X]) (hq : q ≠ 0) : degree p ≤ degree (p * q) := by
+  classical exact
+    if hp : p = 0 then by simp only [hp, MulZeroClass.zero_mul, le_refl]
+    else by
+      rw [degree_mul, degree_eq_nat_degree hp, degree_eq_nat_degree hq] <;>
+        exact WithBot.coe_le_coe.2 (Nat.le_add_right _ _)
 #align polynomial.degree_le_mul_left Polynomial.degree_le_mul_left
 -/
 
@@ -416,7 +428,13 @@ variable [CommRing R]
 /-- The multiplicity of `a` as root of a nonzero polynomial `p` is at least `n` iff
   `(X - a) ^ n` divides `p`. -/
 theorem le_rootMultiplicity_iff {p : R[X]} (p0 : p ≠ 0) {a : R} {n : ℕ} :
-    n ≤ rootMultiplicity a p ↔ (X - C a) ^ n ∣ p := by classical
+    n ≤ rootMultiplicity a p ↔ (X - C a) ^ n ∣ p := by
+  classical
+  simp_rw [root_multiplicity, dif_neg p0, Nat.le_find_iff, Classical.not_not]
+  refine' ⟨fun h => _, fun h m hm => (pow_dvd_pow _ hm).trans h⟩
+  cases n
+  · rw [pow_zero]; apply one_dvd
+  · exact h n n.lt_succ_self
 #align polynomial.le_root_multiplicity_iff Polynomial.le_rootMultiplicity_iff
 -/
 
@@ -502,12 +520,20 @@ theorem eq_of_monic_of_associated (hp : p.Monic) (hq : q.Monic) (hpq : Associate
 
 #print Polynomial.rootMultiplicity_mul /-
 theorem rootMultiplicity_mul {p q : R[X]} {x : R} (hpq : p * q ≠ 0) :
-    rootMultiplicity x (p * q) = rootMultiplicity x p + rootMultiplicity x q := by classical
+    rootMultiplicity x (p * q) = rootMultiplicity x p + rootMultiplicity x q := by
+  classical
+  have hp : p ≠ 0 := left_ne_zero_of_mul hpq
+  have hq : q ≠ 0 := right_ne_zero_of_mul hpq
+  rw [root_multiplicity_eq_multiplicity (p * q), dif_neg hpq, root_multiplicity_eq_multiplicity p,
+    dif_neg hp, root_multiplicity_eq_multiplicity q, dif_neg hq,
+    multiplicity.mul' (prime_X_sub_C x)]
 #align polynomial.root_multiplicity_mul Polynomial.rootMultiplicity_mul
 -/
 
 #print Polynomial.rootMultiplicity_X_sub_C_self /-
-theorem rootMultiplicity_X_sub_C_self {x : R} : rootMultiplicity x (X - C x) = 1 := by classical
+theorem rootMultiplicity_X_sub_C_self {x : R} : rootMultiplicity x (X - C x) = 1 := by
+  classical rw [root_multiplicity_eq_multiplicity, dif_neg (X_sub_C_ne_zero x),
+    multiplicity.get_multiplicity_self]
 #align polynomial.root_multiplicity_X_sub_C_self Polynomial.rootMultiplicity_X_sub_C_self
 -/
 
@@ -603,7 +629,11 @@ theorem roots_zero : (0 : R[X]).roots = 0 := by apply dif_pos rfl
 -/
 
 #print Polynomial.card_roots /-
-theorem card_roots (hp0 : p ≠ 0) : ((roots p).card : WithBot ℕ) ≤ degree p := by classical
+theorem card_roots (hp0 : p ≠ 0) : ((roots p).card : WithBot ℕ) ≤ degree p := by
+  classical
+  unfold roots
+  rw [dif_neg hp0]
+  exact (Classical.choose_spec (exists_multiset_roots hp0)).1
 #align polynomial.card_roots Polynomial.card_roots
 -/
 
@@ -639,12 +669,17 @@ theorem card_roots_sub_C' {p : R[X]} {a : R} (hp0 : 0 < degree p) :
 @[simp]
 theorem count_roots [DecidableEq R] (p : R[X]) : p.roots.count a = rootMultiplicity a p := by
   classical
+  by_cases hp : p = 0
+  · simp [hp]
+  rw [roots_def, dif_neg hp]
+  exact (Classical.choose_spec (exists_multiset_roots hp)).2 a
 #align polynomial.count_roots Polynomial.count_roots
 -/
 
 #print Polynomial.mem_roots' /-
 @[simp]
-theorem mem_roots' : a ∈ p.roots ↔ p ≠ 0 ∧ IsRoot p a := by classical
+theorem mem_roots' : a ∈ p.roots ↔ p ≠ 0 ∧ IsRoot p a := by
+  classical rw [← count_pos, count_roots p, root_multiplicity_pos']
 #align polynomial.mem_roots' Polynomial.mem_roots'
 -/
 
@@ -674,7 +709,9 @@ theorem card_le_degree_of_subset_roots {p : R[X]} {Z : Finset R} (h : Z.val ⊆
 -/
 
 #print Polynomial.finite_setOf_isRoot /-
-theorem finite_setOf_isRoot {p : R[X]} (hp : p ≠ 0) : Set.Finite {x | IsRoot p x} := by classical
+theorem finite_setOf_isRoot {p : R[X]} (hp : p ≠ 0) : Set.Finite {x | IsRoot p x} := by
+  classical simpa only [← Finset.setOf_mem, mem_to_finset, mem_roots hp] using
+    p.roots.to_finset.finite_to_set
 #align polynomial.finite_set_of_is_root Polynomial.finite_setOf_isRoot
 -/
 
@@ -706,7 +743,10 @@ theorem eq_of_infinite_eval_eq (p q : R[X]) (h : Set.Infinite {x | eval x p = ev
 -/
 
 #print Polynomial.roots_mul /-
-theorem roots_mul {p q : R[X]} (hpq : p * q ≠ 0) : (p * q).roots = p.roots + q.roots := by classical
+theorem roots_mul {p q : R[X]} (hpq : p * q ≠ 0) : (p * q).roots = p.roots + q.roots := by
+  classical exact
+    multiset.ext.mpr fun r => by
+      rw [count_add, count_roots, count_roots, count_roots, root_multiplicity_mul hpq]
 #align polynomial.roots_mul Polynomial.roots_mul
 -/
 
@@ -733,7 +773,10 @@ theorem mem_roots_sub_C {p : R[X]} {a x : R} (hp0 : 0 < degree p) :
 
 #print Polynomial.roots_X_sub_C /-
 @[simp]
-theorem roots_X_sub_C (r : R) : roots (X - C r) = {r} := by classical
+theorem roots_X_sub_C (r : R) : roots (X - C r) = {r} := by
+  classical
+  ext s
+  rw [count_roots, root_multiplicity_X_sub_C, count_singleton]
 #align polynomial.roots_X_sub_C Polynomial.roots_X_sub_C
 -/
 
@@ -745,7 +788,12 @@ theorem roots_X : roots (X : R[X]) = {0} := by rw [← roots_X_sub_C, C_0, sub_z
 
 #print Polynomial.roots_C /-
 @[simp]
-theorem roots_C (x : R) : (C x).roots = 0 := by classical
+theorem roots_C (x : R) : (C x).roots = 0 := by
+  classical exact
+    if H : x = 0 then by rw [H, C_0, roots_zero]
+    else
+      multiset.ext.mpr fun r => by
+        rw [count_roots, count_zero, root_multiplicity_eq_zero (not_is_root_C _ _ H)]
 #align polynomial.roots_C Polynomial.roots_C
 -/
 
@@ -896,7 +944,20 @@ theorem nthRoots_zero (r : R) : nthRoots 0 r = 0 := by
 -/
 
 #print Polynomial.card_nthRoots /-
-theorem card_nthRoots (n : ℕ) (a : R) : (nthRoots n a).card ≤ n := by classical
+theorem card_nthRoots (n : ℕ) (a : R) : (nthRoots n a).card ≤ n := by
+  classical exact
+    if hn : n = 0 then
+      if h : (X : R[X]) ^ n - C a = 0 then by
+        simp only [Nat.zero_le, nth_roots, roots, h, dif_pos rfl, empty_eq_zero, Multiset.card_zero]
+      else
+        WithBot.coe_le_coe.1
+          (le_trans (card_roots h)
+            (by
+              rw [hn, pow_zero, ← C_1, ← RingHom.map_sub]
+              exact degree_C_le))
+    else by
+      rw [← WithBot.coe_le_coe, ← degree_X_pow_sub_C (Nat.pos_of_ne_zero hn) a] <;>
+        exact card_roots (X_pow_sub_C_ne_zero (Nat.pos_of_ne_zero hn) a)
 #align polynomial.card_nth_roots Polynomial.card_nthRoots
 -/
 
@@ -985,7 +1046,11 @@ theorem comp_eq_zero_iff : p.comp q = 0 ↔ p = 0 ∨ p.eval (q.coeff 0) = 0 ∧
 -/
 
 #print Polynomial.zero_of_eval_zero /-
-theorem zero_of_eval_zero [Infinite R] (p : R[X]) (h : ∀ x, p.eval x = 0) : p = 0 := by classical
+theorem zero_of_eval_zero [Infinite R] (p : R[X]) (h : ∀ x, p.eval x = 0) : p = 0 := by
+  classical by_contra hp <;>
+    exact
+      Fintype.false
+        ⟨p.roots.to_finset, fun x => multiset.mem_to_finset.mpr ((mem_roots hp).mpr (h _))⟩
 #align polynomial.zero_of_eval_zero Polynomial.zero_of_eval_zero
 -/
 
@@ -1021,7 +1086,7 @@ theorem rootSet_def (p : T[X]) (S) [CommRing S] [IsDomain S] [Algebra T S] [Deci
 #print Polynomial.rootSet_C /-
 @[simp]
 theorem rootSet_C [CommRing S] [IsDomain S] [Algebra T S] (a : T) : (C a).rootSet S = ∅ := by
-  classical
+  classical rw [root_set_def, map_C, roots_C, Multiset.toFinset_zero, Finset.coe_empty]
 #align polynomial.root_set_C Polynomial.rootSet_C
 -/
 
@@ -1245,13 +1310,28 @@ theorem prod_multiset_root_eq_finset_root [DecidableEq R] :
 /-- The product `∏ (X - a)` for `a` inside the multiset `p.roots` divides `p`. -/
 theorem prod_multiset_X_sub_C_dvd (p : R[X]) : (p.roots.map fun a => X - C a).Prod ∣ p := by
   classical
+  rw [← map_dvd_map _ (IsFractionRing.injective R <| FractionRing R) monic_prod_multiset_X_sub_C]
+  rw [prod_multiset_root_eq_finset_root, Polynomial.map_prod]
+  refine' Finset.prod_dvd_of_coprime (fun a _ b _ h => _) fun a _ => _
+  · simp_rw [Polynomial.map_pow, Polynomial.map_sub, map_C, map_X]
+    exact (pairwise_coprime_X_sub_C (IsFractionRing.injective R <| FractionRing R) h).pow
+  · exact Polynomial.map_dvd _ (pow_root_multiplicity_dvd p a)
 #align polynomial.prod_multiset_X_sub_C_dvd Polynomial.prod_multiset_X_sub_C_dvd
 -/
 
 #print Multiset.prod_X_sub_C_dvd_iff_le_roots /-
 /-- A Galois connection. -/
 theorem Multiset.prod_X_sub_C_dvd_iff_le_roots {p : R[X]} (hp : p ≠ 0) (s : Multiset R) :
-    (s.map fun a => X - C a).Prod ∣ p ↔ s ≤ p.roots := by classical
+    (s.map fun a => X - C a).Prod ∣ p ↔ s ≤ p.roots := by
+  classical exact
+    ⟨fun h =>
+      Multiset.le_iff_count.2 fun r =>
+        by
+        rw [count_roots, le_root_multiplicity_iff hp, ← Multiset.prod_replicate, ←
+          Multiset.map_replicate fun a => X - C a, ← Multiset.filter_eq]
+        exact (Multiset.prod_dvd_prod_of_le <| Multiset.map_le_map <| s.filter_le _).trans h,
+      fun h =>
+      (Multiset.prod_dvd_prod_of_le <| Multiset.map_le_map h).trans p.prod_multiset_X_sub_C_dvd⟩
 #align multiset.prod_X_sub_C_dvd_iff_le_roots Multiset.prod_X_sub_C_dvd_iff_le_roots
 -/
 
@@ -1351,7 +1431,8 @@ theorem count_map_roots_of_injective [IsDomain A] [DecidableEq B] (p : A[X]) {f
 
 #print Polynomial.map_roots_le /-
 theorem map_roots_le [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (h : p.map f ≠ 0) :
-    p.roots.map f ≤ (p.map f).roots := by classical
+    p.roots.map f ≤ (p.map f).roots := by
+  classical exact Multiset.le_iff_count.2 fun b => by rw [count_roots]; apply count_map_roots h
 #align polynomial.map_roots_le Polynomial.map_roots_le
 -/
 

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

@@ -172,24 +172,12 @@ theorem trailingDegree_mul : (p * q).trailingDegree = p.trailingDegree + q.trail
 
 #print Polynomial.natDegree_pow /-
 @[simp]
-theorem natDegree_pow (p : R[X]) (n : ℕ) : natDegree (p ^ n) = n * natDegree p := by
-  classical exact
-    if hp0 : p = 0 then
-      if hn0 : n = 0 then by simp [hp0, hn0]
-      else by rw [hp0, zero_pow (Nat.pos_of_ne_zero hn0)] <;> simp
-    else
-      nat_degree_pow'
-        (by rw [← leading_coeff_pow, Ne.def, leading_coeff_eq_zero] <;> exact pow_ne_zero _ hp0)
+theorem natDegree_pow (p : R[X]) (n : ℕ) : natDegree (p ^ n) = n * natDegree p := by classical
 #align polynomial.nat_degree_pow Polynomial.natDegree_pow
 -/
 
 #print Polynomial.degree_le_mul_left /-
-theorem degree_le_mul_left (p : R[X]) (hq : q ≠ 0) : degree p ≤ degree (p * q) := by
-  classical exact
-    if hp : p = 0 then by simp only [hp, MulZeroClass.zero_mul, le_refl]
-    else by
-      rw [degree_mul, degree_eq_nat_degree hp, degree_eq_nat_degree hq] <;>
-        exact WithBot.coe_le_coe.2 (Nat.le_add_right _ _)
+theorem degree_le_mul_left (p : R[X]) (hq : q ≠ 0) : degree p ≤ degree (p * q) := by classical
 #align polynomial.degree_le_mul_left Polynomial.degree_le_mul_left
 -/
 
@@ -428,13 +416,7 @@ variable [CommRing R]
 /-- The multiplicity of `a` as root of a nonzero polynomial `p` is at least `n` iff
   `(X - a) ^ n` divides `p`. -/
 theorem le_rootMultiplicity_iff {p : R[X]} (p0 : p ≠ 0) {a : R} {n : ℕ} :
-    n ≤ rootMultiplicity a p ↔ (X - C a) ^ n ∣ p := by
-  classical
-  simp_rw [root_multiplicity, dif_neg p0, Nat.le_find_iff, Classical.not_not]
-  refine' ⟨fun h => _, fun h m hm => (pow_dvd_pow _ hm).trans h⟩
-  cases n
-  · rw [pow_zero]; apply one_dvd
-  · exact h n n.lt_succ_self
+    n ≤ rootMultiplicity a p ↔ (X - C a) ^ n ∣ p := by classical
 #align polynomial.le_root_multiplicity_iff Polynomial.le_rootMultiplicity_iff
 -/
 
@@ -520,20 +502,12 @@ theorem eq_of_monic_of_associated (hp : p.Monic) (hq : q.Monic) (hpq : Associate
 
 #print Polynomial.rootMultiplicity_mul /-
 theorem rootMultiplicity_mul {p q : R[X]} {x : R} (hpq : p * q ≠ 0) :
-    rootMultiplicity x (p * q) = rootMultiplicity x p + rootMultiplicity x q := by
-  classical
-  have hp : p ≠ 0 := left_ne_zero_of_mul hpq
-  have hq : q ≠ 0 := right_ne_zero_of_mul hpq
-  rw [root_multiplicity_eq_multiplicity (p * q), dif_neg hpq, root_multiplicity_eq_multiplicity p,
-    dif_neg hp, root_multiplicity_eq_multiplicity q, dif_neg hq,
-    multiplicity.mul' (prime_X_sub_C x)]
+    rootMultiplicity x (p * q) = rootMultiplicity x p + rootMultiplicity x q := by classical
 #align polynomial.root_multiplicity_mul Polynomial.rootMultiplicity_mul
 -/
 
 #print Polynomial.rootMultiplicity_X_sub_C_self /-
-theorem rootMultiplicity_X_sub_C_self {x : R} : rootMultiplicity x (X - C x) = 1 := by
-  classical rw [root_multiplicity_eq_multiplicity, dif_neg (X_sub_C_ne_zero x),
-    multiplicity.get_multiplicity_self]
+theorem rootMultiplicity_X_sub_C_self {x : R} : rootMultiplicity x (X - C x) = 1 := by classical
 #align polynomial.root_multiplicity_X_sub_C_self Polynomial.rootMultiplicity_X_sub_C_self
 -/
 
@@ -629,11 +603,7 @@ theorem roots_zero : (0 : R[X]).roots = 0 := by apply dif_pos rfl
 -/
 
 #print Polynomial.card_roots /-
-theorem card_roots (hp0 : p ≠ 0) : ((roots p).card : WithBot ℕ) ≤ degree p := by
-  classical
-  unfold roots
-  rw [dif_neg hp0]
-  exact (Classical.choose_spec (exists_multiset_roots hp0)).1
+theorem card_roots (hp0 : p ≠ 0) : ((roots p).card : WithBot ℕ) ≤ degree p := by classical
 #align polynomial.card_roots Polynomial.card_roots
 -/
 
@@ -669,17 +639,12 @@ theorem card_roots_sub_C' {p : R[X]} {a : R} (hp0 : 0 < degree p) :
 @[simp]
 theorem count_roots [DecidableEq R] (p : R[X]) : p.roots.count a = rootMultiplicity a p := by
   classical
-  by_cases hp : p = 0
-  · simp [hp]
-  rw [roots_def, dif_neg hp]
-  exact (Classical.choose_spec (exists_multiset_roots hp)).2 a
 #align polynomial.count_roots Polynomial.count_roots
 -/
 
 #print Polynomial.mem_roots' /-
 @[simp]
-theorem mem_roots' : a ∈ p.roots ↔ p ≠ 0 ∧ IsRoot p a := by
-  classical rw [← count_pos, count_roots p, root_multiplicity_pos']
+theorem mem_roots' : a ∈ p.roots ↔ p ≠ 0 ∧ IsRoot p a := by classical
 #align polynomial.mem_roots' Polynomial.mem_roots'
 -/
 
@@ -709,9 +674,7 @@ theorem card_le_degree_of_subset_roots {p : R[X]} {Z : Finset R} (h : Z.val ⊆
 -/
 
 #print Polynomial.finite_setOf_isRoot /-
-theorem finite_setOf_isRoot {p : R[X]} (hp : p ≠ 0) : Set.Finite {x | IsRoot p x} := by
-  classical simpa only [← Finset.setOf_mem, mem_to_finset, mem_roots hp] using
-    p.roots.to_finset.finite_to_set
+theorem finite_setOf_isRoot {p : R[X]} (hp : p ≠ 0) : Set.Finite {x | IsRoot p x} := by classical
 #align polynomial.finite_set_of_is_root Polynomial.finite_setOf_isRoot
 -/
 
@@ -743,10 +706,7 @@ theorem eq_of_infinite_eval_eq (p q : R[X]) (h : Set.Infinite {x | eval x p = ev
 -/
 
 #print Polynomial.roots_mul /-
-theorem roots_mul {p q : R[X]} (hpq : p * q ≠ 0) : (p * q).roots = p.roots + q.roots := by
-  classical exact
-    multiset.ext.mpr fun r => by
-      rw [count_add, count_roots, count_roots, count_roots, root_multiplicity_mul hpq]
+theorem roots_mul {p q : R[X]} (hpq : p * q ≠ 0) : (p * q).roots = p.roots + q.roots := by classical
 #align polynomial.roots_mul Polynomial.roots_mul
 -/
 
@@ -773,10 +733,7 @@ theorem mem_roots_sub_C {p : R[X]} {a x : R} (hp0 : 0 < degree p) :
 
 #print Polynomial.roots_X_sub_C /-
 @[simp]
-theorem roots_X_sub_C (r : R) : roots (X - C r) = {r} := by
-  classical
-  ext s
-  rw [count_roots, root_multiplicity_X_sub_C, count_singleton]
+theorem roots_X_sub_C (r : R) : roots (X - C r) = {r} := by classical
 #align polynomial.roots_X_sub_C Polynomial.roots_X_sub_C
 -/
 
@@ -788,12 +745,7 @@ theorem roots_X : roots (X : R[X]) = {0} := by rw [← roots_X_sub_C, C_0, sub_z
 
 #print Polynomial.roots_C /-
 @[simp]
-theorem roots_C (x : R) : (C x).roots = 0 := by
-  classical exact
-    if H : x = 0 then by rw [H, C_0, roots_zero]
-    else
-      multiset.ext.mpr fun r => by
-        rw [count_roots, count_zero, root_multiplicity_eq_zero (not_is_root_C _ _ H)]
+theorem roots_C (x : R) : (C x).roots = 0 := by classical
 #align polynomial.roots_C Polynomial.roots_C
 -/
 
@@ -944,20 +896,7 @@ theorem nthRoots_zero (r : R) : nthRoots 0 r = 0 := by
 -/
 
 #print Polynomial.card_nthRoots /-
-theorem card_nthRoots (n : ℕ) (a : R) : (nthRoots n a).card ≤ n := by
-  classical exact
-    if hn : n = 0 then
-      if h : (X : R[X]) ^ n - C a = 0 then by
-        simp only [Nat.zero_le, nth_roots, roots, h, dif_pos rfl, empty_eq_zero, Multiset.card_zero]
-      else
-        WithBot.coe_le_coe.1
-          (le_trans (card_roots h)
-            (by
-              rw [hn, pow_zero, ← C_1, ← RingHom.map_sub]
-              exact degree_C_le))
-    else by
-      rw [← WithBot.coe_le_coe, ← degree_X_pow_sub_C (Nat.pos_of_ne_zero hn) a] <;>
-        exact card_roots (X_pow_sub_C_ne_zero (Nat.pos_of_ne_zero hn) a)
+theorem card_nthRoots (n : ℕ) (a : R) : (nthRoots n a).card ≤ n := by classical
 #align polynomial.card_nth_roots Polynomial.card_nthRoots
 -/
 
@@ -1046,11 +985,7 @@ theorem comp_eq_zero_iff : p.comp q = 0 ↔ p = 0 ∨ p.eval (q.coeff 0) = 0 ∧
 -/
 
 #print Polynomial.zero_of_eval_zero /-
-theorem zero_of_eval_zero [Infinite R] (p : R[X]) (h : ∀ x, p.eval x = 0) : p = 0 := by
-  classical by_contra hp <;>
-    exact
-      Fintype.false
-        ⟨p.roots.to_finset, fun x => multiset.mem_to_finset.mpr ((mem_roots hp).mpr (h _))⟩
+theorem zero_of_eval_zero [Infinite R] (p : R[X]) (h : ∀ x, p.eval x = 0) : p = 0 := by classical
 #align polynomial.zero_of_eval_zero Polynomial.zero_of_eval_zero
 -/
 
@@ -1086,7 +1021,7 @@ theorem rootSet_def (p : T[X]) (S) [CommRing S] [IsDomain S] [Algebra T S] [Deci
 #print Polynomial.rootSet_C /-
 @[simp]
 theorem rootSet_C [CommRing S] [IsDomain S] [Algebra T S] (a : T) : (C a).rootSet S = ∅ := by
-  classical rw [root_set_def, map_C, roots_C, Multiset.toFinset_zero, Finset.coe_empty]
+  classical
 #align polynomial.root_set_C Polynomial.rootSet_C
 -/
 
@@ -1310,28 +1245,13 @@ theorem prod_multiset_root_eq_finset_root [DecidableEq R] :
 /-- The product `∏ (X - a)` for `a` inside the multiset `p.roots` divides `p`. -/
 theorem prod_multiset_X_sub_C_dvd (p : R[X]) : (p.roots.map fun a => X - C a).Prod ∣ p := by
   classical
-  rw [← map_dvd_map _ (IsFractionRing.injective R <| FractionRing R) monic_prod_multiset_X_sub_C]
-  rw [prod_multiset_root_eq_finset_root, Polynomial.map_prod]
-  refine' Finset.prod_dvd_of_coprime (fun a _ b _ h => _) fun a _ => _
-  · simp_rw [Polynomial.map_pow, Polynomial.map_sub, map_C, map_X]
-    exact (pairwise_coprime_X_sub_C (IsFractionRing.injective R <| FractionRing R) h).pow
-  · exact Polynomial.map_dvd _ (pow_root_multiplicity_dvd p a)
 #align polynomial.prod_multiset_X_sub_C_dvd Polynomial.prod_multiset_X_sub_C_dvd
 -/
 
 #print Multiset.prod_X_sub_C_dvd_iff_le_roots /-
 /-- A Galois connection. -/
 theorem Multiset.prod_X_sub_C_dvd_iff_le_roots {p : R[X]} (hp : p ≠ 0) (s : Multiset R) :
-    (s.map fun a => X - C a).Prod ∣ p ↔ s ≤ p.roots := by
-  classical exact
-    ⟨fun h =>
-      Multiset.le_iff_count.2 fun r =>
-        by
-        rw [count_roots, le_root_multiplicity_iff hp, ← Multiset.prod_replicate, ←
-          Multiset.map_replicate fun a => X - C a, ← Multiset.filter_eq]
-        exact (Multiset.prod_dvd_prod_of_le <| Multiset.map_le_map <| s.filter_le _).trans h,
-      fun h =>
-      (Multiset.prod_dvd_prod_of_le <| Multiset.map_le_map h).trans p.prod_multiset_X_sub_C_dvd⟩
+    (s.map fun a => X - C a).Prod ∣ p ↔ s ≤ p.roots := by classical
 #align multiset.prod_X_sub_C_dvd_iff_le_roots Multiset.prod_X_sub_C_dvd_iff_le_roots
 -/
 
@@ -1431,8 +1351,7 @@ theorem count_map_roots_of_injective [IsDomain A] [DecidableEq B] (p : A[X]) {f
 
 #print Polynomial.map_roots_le /-
 theorem map_roots_le [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (h : p.map f ≠ 0) :
-    p.roots.map f ≤ (p.map f).roots := by
-  classical exact Multiset.le_iff_count.2 fun b => by rw [count_roots]; apply count_map_roots h
+    p.roots.map f ≤ (p.map f).roots := by classical
 #align polynomial.map_roots_le Polynomial.map_roots_le
 -/
 

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

@@ -704,7 +704,7 @@ theorem isRoot_of_mem_roots (h : a ∈ p.roots) : IsRoot p a :=
 #print Polynomial.card_le_degree_of_subset_roots /-
 theorem card_le_degree_of_subset_roots {p : R[X]} {Z : Finset R} (h : Z.val ⊆ p.roots) :
     Z.card ≤ p.natDegree :=
-  (Multiset.card_le_of_le (Finset.val_le_iff_val_subset.2 h)).trans (Polynomial.card_roots' p)
+  (Multiset.card_le_card (Finset.val_le_iff_val_subset.2 h)).trans (Polynomial.card_roots' p)
 #align polynomial.card_le_degree_of_subset_roots Polynomial.card_le_degree_of_subset_roots
 -/
 
@@ -1448,7 +1448,7 @@ theorem map_roots_le_of_injective [IsDomain A] [IsDomain B] (p : A[X]) {f : A 
 #print Polynomial.card_roots_le_map /-
 theorem card_roots_le_map [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (h : p.map f ≠ 0) :
     p.roots.card ≤ (p.map f).roots.card := by rw [← p.roots.card_map f];
-  exact Multiset.card_le_of_le (map_roots_le h)
+  exact Multiset.card_le_card (map_roots_le h)
 #align polynomial.card_roots_le_map Polynomial.card_roots_le_map
 -/
 

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

@@ -3,12 +3,12 @@ Copyright (c) 2018 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker, Johan Commelin
 -/
-import Mathbin.Algebra.CharZero.Infinite
-import Mathbin.Data.Polynomial.AlgebraMap
-import Mathbin.Data.Polynomial.Degree.Lemmas
-import Mathbin.Data.Polynomial.Div
-import Mathbin.RingTheory.Localization.FractionRing
-import Mathbin.Algebra.Polynomial.BigOperators
+import Algebra.CharZero.Infinite
+import Data.Polynomial.AlgebraMap
+import Data.Polynomial.Degree.Lemmas
+import Data.Polynomial.Div
+import RingTheory.Localization.FractionRing
+import Algebra.Polynomial.BigOperators
 
 #align_import data.polynomial.ring_division from "leanprover-community/mathlib"@"8efcf8022aac8e01df8d302dcebdbc25d6a886c8"
 

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

@@ -2,11 +2,6 @@
 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, Johan Commelin
-
-! This file was ported from Lean 3 source module data.polynomial.ring_division
-! leanprover-community/mathlib commit 8efcf8022aac8e01df8d302dcebdbc25d6a886c8
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.CharZero.Infinite
 import Mathbin.Data.Polynomial.AlgebraMap
@@ -15,6 +10,8 @@ import Mathbin.Data.Polynomial.Div
 import Mathbin.RingTheory.Localization.FractionRing
 import Mathbin.Algebra.Polynomial.BigOperators
 
+#align_import data.polynomial.ring_division from "leanprover-community/mathlib"@"8efcf8022aac8e01df8d302dcebdbc25d6a886c8"
+
 /-!
 # Theory of univariate polynomials
 

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

@@ -615,6 +615,7 @@ noncomputable def roots (p : R[X]) : Multiset R := by
 #align polynomial.roots Polynomial.roots
 -/
 
+#print Polynomial.roots_def /-
 theorem roots_def [DecidableEq R] (p : R[X]) [Decidable (p = 0)] :
     p.roots = if h : p = 0 then ∅ else Classical.choose (exists_multiset_roots h) :=
   by
@@ -622,6 +623,7 @@ theorem roots_def [DecidableEq R] (p : R[X]) [Decidable (p = 0)] :
   obtain rfl := Subsingleton.elim ‹_› (Classical.dec (p = 0))
   rfl
 #align polynomial.roots_def Polynomial.roots_def
+-/
 
 #print Polynomial.roots_zero /-
 @[simp]

mathlib commit https://github.com/leanprover-community/mathlib/commit/8efcf8022aac8e01df8d302dcebdbc25d6a886c8

@@ -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, Johan Commelin
 
 ! This file was ported from Lean 3 source module data.polynomial.ring_division
-! leanprover-community/mathlib commit 517cc149e0b515d2893baa376226ed10feb319c7
+! leanprover-community/mathlib commit 8efcf8022aac8e01df8d302dcebdbc25d6a886c8
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -40,7 +40,7 @@ This file starts looking like the ring theory of $ R[X] $
 
 noncomputable section
 
-open scoped Classical Polynomial
+open scoped Polynomial
 
 open Finset
 
@@ -175,22 +175,24 @@ theorem trailingDegree_mul : (p * q).trailingDegree = p.trailingDegree + q.trail
 
 #print Polynomial.natDegree_pow /-
 @[simp]
-theorem natDegree_pow (p : R[X]) (n : ℕ) : natDegree (p ^ n) = n * natDegree p :=
-  if hp0 : p = 0 then
-    if hn0 : n = 0 then by simp [hp0, hn0]
-    else by rw [hp0, zero_pow (Nat.pos_of_ne_zero hn0)] <;> simp
-  else
-    natDegree_pow'
-      (by rw [← leading_coeff_pow, Ne.def, leading_coeff_eq_zero] <;> exact pow_ne_zero _ hp0)
+theorem natDegree_pow (p : R[X]) (n : ℕ) : natDegree (p ^ n) = n * natDegree p := by
+  classical exact
+    if hp0 : p = 0 then
+      if hn0 : n = 0 then by simp [hp0, hn0]
+      else by rw [hp0, zero_pow (Nat.pos_of_ne_zero hn0)] <;> simp
+    else
+      nat_degree_pow'
+        (by rw [← leading_coeff_pow, Ne.def, leading_coeff_eq_zero] <;> exact pow_ne_zero _ hp0)
 #align polynomial.nat_degree_pow Polynomial.natDegree_pow
 -/
 
 #print Polynomial.degree_le_mul_left /-
-theorem degree_le_mul_left (p : R[X]) (hq : q ≠ 0) : degree p ≤ degree (p * q) :=
-  if hp : p = 0 then by simp only [hp, MulZeroClass.zero_mul, le_refl]
-  else by
-    rw [degree_mul, degree_eq_nat_degree hp, degree_eq_nat_degree hq] <;>
-      exact WithBot.coe_le_coe.2 (Nat.le_add_right _ _)
+theorem degree_le_mul_left (p : R[X]) (hq : q ≠ 0) : degree p ≤ degree (p * q) := by
+  classical exact
+    if hp : p = 0 then by simp only [hp, MulZeroClass.zero_mul, le_refl]
+    else by
+      rw [degree_mul, degree_eq_nat_degree hp, degree_eq_nat_degree hq] <;>
+        exact WithBot.coe_le_coe.2 (Nat.le_add_right _ _)
 #align polynomial.degree_le_mul_left Polynomial.degree_le_mul_left
 -/
 
@@ -429,11 +431,13 @@ variable [CommRing R]
 /-- The multiplicity of `a` as root of a nonzero polynomial `p` is at least `n` iff
   `(X - a) ^ n` divides `p`. -/
 theorem le_rootMultiplicity_iff {p : R[X]} (p0 : p ≠ 0) {a : R} {n : ℕ} :
-    n ≤ rootMultiplicity a p ↔ (X - C a) ^ n ∣ p :=
-  by
+    n ≤ rootMultiplicity a p ↔ (X - C a) ^ n ∣ p := by
+  classical
   simp_rw [root_multiplicity, dif_neg p0, Nat.le_find_iff, Classical.not_not]
   refine' ⟨fun h => _, fun h m hm => (pow_dvd_pow _ hm).trans h⟩
-  cases n; · rw [pow_zero]; apply one_dvd; · exact h n n.lt_succ_self
+  cases n
+  · rw [pow_zero]; apply one_dvd
+  · exact h n n.lt_succ_self
 #align polynomial.le_root_multiplicity_iff Polynomial.le_rootMultiplicity_iff
 -/
 
@@ -519,8 +523,8 @@ theorem eq_of_monic_of_associated (hp : p.Monic) (hq : q.Monic) (hpq : Associate
 
 #print Polynomial.rootMultiplicity_mul /-
 theorem rootMultiplicity_mul {p q : R[X]} {x : R} (hpq : p * q ≠ 0) :
-    rootMultiplicity x (p * q) = rootMultiplicity x p + rootMultiplicity x q :=
-  by
+    rootMultiplicity x (p * q) = rootMultiplicity x p + rootMultiplicity x q := by
+  classical
   have hp : p ≠ 0 := left_ne_zero_of_mul hpq
   have hq : q ≠ 0 := right_ne_zero_of_mul hpq
   rw [root_multiplicity_eq_multiplicity (p * q), dif_neg hpq, root_multiplicity_eq_multiplicity p,
@@ -531,13 +535,13 @@ theorem rootMultiplicity_mul {p q : R[X]} {x : R} (hpq : p * q ≠ 0) :
 
 #print Polynomial.rootMultiplicity_X_sub_C_self /-
 theorem rootMultiplicity_X_sub_C_self {x : R} : rootMultiplicity x (X - C x) = 1 := by
-  rw [root_multiplicity_eq_multiplicity, dif_neg (X_sub_C_ne_zero x),
+  classical rw [root_multiplicity_eq_multiplicity, dif_neg (X_sub_C_ne_zero x),
     multiplicity.get_multiplicity_self]
 #align polynomial.root_multiplicity_X_sub_C_self Polynomial.rootMultiplicity_X_sub_C_self
 -/
 
 #print Polynomial.rootMultiplicity_X_sub_C /-
-theorem rootMultiplicity_X_sub_C {x y : R} :
+theorem rootMultiplicity_X_sub_C {x y : R} [DecidableEq R] :
     rootMultiplicity x (X - C y) = if x = y then 1 else 0 :=
   by
   split_ifs with hxy
@@ -561,7 +565,7 @@ theorem rootMultiplicity_X_sub_C_pow (a : R) (n : ℕ) : rootMultiplicity a ((X
 -/
 
 #print Polynomial.exists_multiset_roots /-
-theorem exists_multiset_roots :
+theorem exists_multiset_roots [DecidableEq R] :
     ∀ {p : R[X]} (hp : p ≠ 0),
       ∃ s : Multiset R, (s.card : WithBot ℕ) ≤ degree p ∧ ∀ a, s.count a = rootMultiplicity a p
   | p => fun hp =>
@@ -605,21 +609,29 @@ theorem exists_multiset_roots :
 #print Polynomial.roots /-
 /-- `roots p` noncomputably gives a multiset containing all the roots of `p`,
 including their multiplicities. -/
-noncomputable def roots (p : R[X]) : Multiset R :=
-  if h : p = 0 then ∅ else Classical.choose (exists_multiset_roots h)
+noncomputable def roots (p : R[X]) : Multiset R := by
+  haveI := Classical.decEq R <;> haveI := Classical.dec (p = 0) <;>
+    exact if h : p = 0 then ∅ else Classical.choose (exists_multiset_roots h)
 #align polynomial.roots Polynomial.roots
 -/
 
+theorem roots_def [DecidableEq R] (p : R[X]) [Decidable (p = 0)] :
+    p.roots = if h : p = 0 then ∅ else Classical.choose (exists_multiset_roots h) :=
+  by
+  obtain rfl := Subsingleton.elim ‹_› (Classical.decEq R)
+  obtain rfl := Subsingleton.elim ‹_› (Classical.dec (p = 0))
+  rfl
+#align polynomial.roots_def Polynomial.roots_def
+
 #print Polynomial.roots_zero /-
 @[simp]
-theorem roots_zero : (0 : R[X]).roots = 0 :=
-  dif_pos rfl
+theorem roots_zero : (0 : R[X]).roots = 0 := by apply dif_pos rfl
 #align polynomial.roots_zero Polynomial.roots_zero
 -/
 
 #print Polynomial.card_roots /-
-theorem card_roots (hp0 : p ≠ 0) : ((roots p).card : WithBot ℕ) ≤ degree p :=
-  by
+theorem card_roots (hp0 : p ≠ 0) : ((roots p).card : WithBot ℕ) ≤ degree p := by
+  classical
   unfold roots
   rw [dif_neg hp0]
   exact (Classical.choose_spec (exists_multiset_roots hp0)).1
@@ -656,11 +668,11 @@ theorem card_roots_sub_C' {p : R[X]} {a : R} (hp0 : 0 < degree p) :
 
 #print Polynomial.count_roots /-
 @[simp]
-theorem count_roots (p : R[X]) : p.roots.count a = rootMultiplicity a p :=
-  by
+theorem count_roots [DecidableEq R] (p : R[X]) : p.roots.count a = rootMultiplicity a p := by
+  classical
   by_cases hp : p = 0
   · simp [hp]
-  rw [roots, dif_neg hp]
+  rw [roots_def, dif_neg hp]
   exact (Classical.choose_spec (exists_multiset_roots hp)).2 a
 #align polynomial.count_roots Polynomial.count_roots
 -/
@@ -668,7 +680,7 @@ theorem count_roots (p : R[X]) : p.roots.count a = rootMultiplicity a p :=
 #print Polynomial.mem_roots' /-
 @[simp]
 theorem mem_roots' : a ∈ p.roots ↔ p ≠ 0 ∧ IsRoot p a := by
-  rw [← count_pos, count_roots p, root_multiplicity_pos']
+  classical rw [← count_pos, count_roots p, root_multiplicity_pos']
 #align polynomial.mem_roots' Polynomial.mem_roots'
 -/
 
@@ -699,7 +711,8 @@ theorem card_le_degree_of_subset_roots {p : R[X]} {Z : Finset R} (h : Z.val ⊆
 
 #print Polynomial.finite_setOf_isRoot /-
 theorem finite_setOf_isRoot {p : R[X]} (hp : p ≠ 0) : Set.Finite {x | IsRoot p x} := by
-  simpa only [← Finset.setOf_mem, mem_to_finset, mem_roots hp] using p.roots.to_finset.finite_to_set
+  classical simpa only [← Finset.setOf_mem, mem_to_finset, mem_roots hp] using
+    p.roots.to_finset.finite_to_set
 #align polynomial.finite_set_of_is_root Polynomial.finite_setOf_isRoot
 -/
 
@@ -731,9 +744,10 @@ theorem eq_of_infinite_eval_eq (p q : R[X]) (h : Set.Infinite {x | eval x p = ev
 -/
 
 #print Polynomial.roots_mul /-
-theorem roots_mul {p q : R[X]} (hpq : p * q ≠ 0) : (p * q).roots = p.roots + q.roots :=
-  Multiset.ext.mpr fun r => by
-    rw [count_add, count_roots, count_roots, count_roots, root_multiplicity_mul hpq]
+theorem roots_mul {p q : R[X]} (hpq : p * q ≠ 0) : (p * q).roots = p.roots + q.roots := by
+  classical exact
+    multiset.ext.mpr fun r => by
+      rw [count_add, count_roots, count_roots, count_roots, root_multiplicity_mul hpq]
 #align polynomial.roots_mul Polynomial.roots_mul
 -/
 
@@ -760,8 +774,8 @@ theorem mem_roots_sub_C {p : R[X]} {a x : R} (hp0 : 0 < degree p) :
 
 #print Polynomial.roots_X_sub_C /-
 @[simp]
-theorem roots_X_sub_C (r : R) : roots (X - C r) = {r} :=
-  by
+theorem roots_X_sub_C (r : R) : roots (X - C r) = {r} := by
+  classical
   ext s
   rw [count_roots, root_multiplicity_X_sub_C, count_singleton]
 #align polynomial.roots_X_sub_C Polynomial.roots_X_sub_C
@@ -775,11 +789,12 @@ theorem roots_X : roots (X : R[X]) = {0} := by rw [← roots_X_sub_C, C_0, sub_z
 
 #print Polynomial.roots_C /-
 @[simp]
-theorem roots_C (x : R) : (C x).roots = 0 :=
-  if H : x = 0 then by rw [H, C_0, roots_zero]
-  else
-    Multiset.ext.mpr fun r => by
-      rw [count_roots, count_zero, root_multiplicity_eq_zero (not_is_root_C _ _ H)]
+theorem roots_C (x : R) : (C x).roots = 0 := by
+  classical exact
+    if H : x = 0 then by rw [H, C_0, roots_zero]
+    else
+      multiset.ext.mpr fun r => by
+        rw [count_roots, count_zero, root_multiplicity_eq_zero (not_is_root_C _ _ H)]
 #align polynomial.roots_C Polynomial.roots_C
 -/
 
@@ -930,19 +945,20 @@ theorem nthRoots_zero (r : R) : nthRoots 0 r = 0 := by
 -/
 
 #print Polynomial.card_nthRoots /-
-theorem card_nthRoots (n : ℕ) (a : R) : (nthRoots n a).card ≤ n :=
-  if hn : n = 0 then
-    if h : (X : R[X]) ^ n - C a = 0 then by
-      simp only [Nat.zero_le, nth_roots, roots, h, dif_pos rfl, empty_eq_zero, Multiset.card_zero]
-    else
-      WithBot.coe_le_coe.1
-        (le_trans (card_roots h)
-          (by
-            rw [hn, pow_zero, ← C_1, ← RingHom.map_sub]
-            exact degree_C_le))
-  else by
-    rw [← WithBot.coe_le_coe, ← degree_X_pow_sub_C (Nat.pos_of_ne_zero hn) a] <;>
-      exact card_roots (X_pow_sub_C_ne_zero (Nat.pos_of_ne_zero hn) a)
+theorem card_nthRoots (n : ℕ) (a : R) : (nthRoots n a).card ≤ n := by
+  classical exact
+    if hn : n = 0 then
+      if h : (X : R[X]) ^ n - C a = 0 then by
+        simp only [Nat.zero_le, nth_roots, roots, h, dif_pos rfl, empty_eq_zero, Multiset.card_zero]
+      else
+        WithBot.coe_le_coe.1
+          (le_trans (card_roots h)
+            (by
+              rw [hn, pow_zero, ← C_1, ← RingHom.map_sub]
+              exact degree_C_le))
+    else by
+      rw [← WithBot.coe_le_coe, ← degree_X_pow_sub_C (Nat.pos_of_ne_zero hn) a] <;>
+        exact card_roots (X_pow_sub_C_ne_zero (Nat.pos_of_ne_zero hn) a)
 #align polynomial.card_nth_roots Polynomial.card_nthRoots
 -/
 
@@ -957,7 +973,8 @@ theorem nthRoots_two_eq_zero_iff {r : R} : nthRoots 2 r = 0 ↔ ¬IsSquare r :=
 #print Polynomial.nthRootsFinset /-
 /-- The multiset `nth_roots ↑n (1 : R)` as a finset. -/
 def nthRootsFinset (n : ℕ) (R : Type _) [CommRing R] [IsDomain R] : Finset R :=
-  Multiset.toFinset (nthRoots n (1 : R))
+  haveI := Classical.decEq R
+  Multiset.toFinset (nth_roots n (1 : R))
 #align polynomial.nth_roots_finset Polynomial.nthRootsFinset
 -/
 
@@ -1056,21 +1073,21 @@ variable [CommRing T]
 If you have a non-separable polynomial, use `polynomial.roots` for the multiset
 where multiple roots have the appropriate multiplicity. -/
 def rootSet (p : T[X]) (S) [CommRing S] [IsDomain S] [Algebra T S] : Set S :=
+  haveI := Classical.decEq S
   (p.map (algebraMap T S)).roots.toFinset
 #align polynomial.root_set Polynomial.rootSet
 -/
 
 #print Polynomial.rootSet_def /-
-theorem rootSet_def (p : T[X]) (S) [CommRing S] [IsDomain S] [Algebra T S] :
-    p.rootSet S = (p.map (algebraMap T S)).roots.toFinset :=
-  rfl
+theorem rootSet_def (p : T[X]) (S) [CommRing S] [IsDomain S] [Algebra T S] [DecidableEq S] :
+    p.rootSet S = (p.map (algebraMap T S)).roots.toFinset := by convert rfl
 #align polynomial.root_set_def Polynomial.rootSet_def
 -/
 
 #print Polynomial.rootSet_C /-
 @[simp]
 theorem rootSet_C [CommRing S] [IsDomain S] [Algebra T S] (a : T) : (C a).rootSet S = ∅ := by
-  rw [root_set_def, map_C, roots_C, Multiset.toFinset_zero, Finset.coe_empty]
+  classical rw [root_set_def, map_C, roots_C, Multiset.toFinset_zero, Finset.coe_empty]
 #align polynomial.root_set_C Polynomial.rootSet_C
 -/
 
@@ -1098,8 +1115,8 @@ theorem rootSet_finite (p : T[X]) (S : Type _) [CommRing S] [IsDomain S] [Algebr
 #print Polynomial.bUnion_roots_finite /-
 /-- The set of roots of all polynomials of bounded degree and having coefficients in a finite set
 is finite. -/
-theorem bUnion_roots_finite {R S : Type _} [Semiring R] [CommRing S] [IsDomain S] (m : R →+* S)
-    (d : ℕ) {U : Set R} (h : U.Finite) :
+theorem bUnion_roots_finite {R S : Type _} [Semiring R] [CommRing S] [IsDomain S] [DecidableEq S]
+    (m : R →+* S) (d : ℕ) {U : Set R} (h : U.Finite) :
     (⋃ (f : R[X]) (hf : f.natDegree ≤ d ∧ ∀ i, f.coeff i ∈ U),
         ((f.map m).roots.toFinset : Set S)).Finite :=
   Set.Finite.biUnion
@@ -1283,7 +1300,7 @@ theorem monic_prod_multiset_X_sub_C : Monic (p.roots.map fun a => X - C a).Prod
 -/
 
 #print Polynomial.prod_multiset_root_eq_finset_root /-
-theorem prod_multiset_root_eq_finset_root :
+theorem prod_multiset_root_eq_finset_root [DecidableEq R] :
     (p.roots.map fun a => X - C a).Prod =
       p.roots.toFinset.Prod fun a => (X - C a) ^ rootMultiplicity a p :=
   by simp only [count_roots, Finset.prod_multiset_map_count]
@@ -1292,8 +1309,8 @@ theorem prod_multiset_root_eq_finset_root :
 
 #print Polynomial.prod_multiset_X_sub_C_dvd /-
 /-- The product `∏ (X - a)` for `a` inside the multiset `p.roots` divides `p`. -/
-theorem prod_multiset_X_sub_C_dvd (p : R[X]) : (p.roots.map fun a => X - C a).Prod ∣ p :=
-  by
+theorem prod_multiset_X_sub_C_dvd (p : R[X]) : (p.roots.map fun a => X - C a).Prod ∣ p := by
+  classical
   rw [← map_dvd_map _ (IsFractionRing.injective R <| FractionRing R) monic_prod_multiset_X_sub_C]
   rw [prod_multiset_root_eq_finset_root, Polynomial.map_prod]
   refine' Finset.prod_dvd_of_coprime (fun a _ b _ h => _) fun a _ => _
@@ -1306,15 +1323,16 @@ theorem prod_multiset_X_sub_C_dvd (p : R[X]) : (p.roots.map fun a => X - C a).Pr
 #print Multiset.prod_X_sub_C_dvd_iff_le_roots /-
 /-- A Galois connection. -/
 theorem Multiset.prod_X_sub_C_dvd_iff_le_roots {p : R[X]} (hp : p ≠ 0) (s : Multiset R) :
-    (s.map fun a => X - C a).Prod ∣ p ↔ s ≤ p.roots :=
-  ⟨fun h =>
-    Multiset.le_iff_count.2 fun r =>
-      by
-      rw [count_roots, le_root_multiplicity_iff hp, ← Multiset.prod_replicate, ←
-        Multiset.map_replicate fun a => X - C a, ← Multiset.filter_eq]
-      exact (Multiset.prod_dvd_prod_of_le <| Multiset.map_le_map <| s.filter_le _).trans h,
-    fun h =>
-    (Multiset.prod_dvd_prod_of_le <| Multiset.map_le_map h).trans p.prod_multiset_X_sub_C_dvd⟩
+    (s.map fun a => X - C a).Prod ∣ p ↔ s ≤ p.roots := by
+  classical exact
+    ⟨fun h =>
+      Multiset.le_iff_count.2 fun r =>
+        by
+        rw [count_roots, le_root_multiplicity_iff hp, ← Multiset.prod_replicate, ←
+          Multiset.map_replicate fun a => X - C a, ← Multiset.filter_eq]
+        exact (Multiset.prod_dvd_prod_of_le <| Multiset.map_le_map <| s.filter_le _).trans h,
+      fun h =>
+      (Multiset.prod_dvd_prod_of_le <| Multiset.map_le_map h).trans p.prod_multiset_X_sub_C_dvd⟩
 #align multiset.prod_X_sub_C_dvd_iff_le_roots Multiset.prod_X_sub_C_dvd_iff_le_roots
 -/
 
@@ -1386,8 +1404,8 @@ theorem eq_rootMultiplicity_map {p : A[X]} {f : A →+* B} (hf : Function.Inject
 -/
 
 #print Polynomial.count_map_roots /-
-theorem count_map_roots [IsDomain A] {p : A[X]} {f : A →+* B} (hmap : map f p ≠ 0) (b : B) :
-    (p.roots.map f).count b ≤ rootMultiplicity b (p.map f) :=
+theorem count_map_roots [IsDomain A] [DecidableEq B] {p : A[X]} {f : A →+* B} (hmap : map f p ≠ 0)
+    (b : B) : (p.roots.map f).count b ≤ rootMultiplicity b (p.map f) :=
   by
   rw [le_root_multiplicity_iff hmap, ← Multiset.prod_replicate, ←
     Multiset.map_replicate fun a => X - C a]
@@ -1401,7 +1419,7 @@ theorem count_map_roots [IsDomain A] {p : A[X]} {f : A →+* B} (hmap : map f p
 -/
 
 #print Polynomial.count_map_roots_of_injective /-
-theorem count_map_roots_of_injective [IsDomain A] (p : A[X]) {f : A →+* B}
+theorem count_map_roots_of_injective [IsDomain A] [DecidableEq B] (p : A[X]) {f : A →+* B}
     (hf : Function.Injective f) (b : B) : (p.roots.map f).count b ≤ rootMultiplicity b (p.map f) :=
   by
   by_cases hp0 : p = 0
@@ -1414,8 +1432,8 @@ theorem count_map_roots_of_injective [IsDomain A] (p : A[X]) {f : A →+* B}
 
 #print Polynomial.map_roots_le /-
 theorem map_roots_le [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (h : p.map f ≠ 0) :
-    p.roots.map f ≤ (p.map f).roots :=
-  Multiset.le_iff_count.2 fun b => by rw [count_roots]; apply count_map_roots h
+    p.roots.map f ≤ (p.map f).roots := by
+  classical exact Multiset.le_iff_count.2 fun b => by rw [count_roots]; apply count_map_roots h
 #align polynomial.map_roots_le Polynomial.map_roots_le
 -/
 

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

@@ -58,15 +58,19 @@ section
 
 variable [Semiring S]
 
+#print Polynomial.natDegree_pos_of_aeval_root /-
 theorem natDegree_pos_of_aeval_root [Algebra R S] {p : R[X]} (hp : p ≠ 0) {z : S}
     (hz : aeval z p = 0) (inj : ∀ x : R, algebraMap R S x = 0 → x = 0) : 0 < p.natDegree :=
   natDegree_pos_of_eval₂_root hp (algebraMap R S) hz inj
 #align polynomial.nat_degree_pos_of_aeval_root Polynomial.natDegree_pos_of_aeval_root
+-/
 
+#print Polynomial.degree_pos_of_aeval_root /-
 theorem degree_pos_of_aeval_root [Algebra R S] {p : R[X]} (hp : p ≠ 0) {z : S} (hz : aeval z p = 0)
     (inj : ∀ x : R, algebraMap R S x = 0 → x = 0) : 0 < p.degree :=
   natDegree_pos_iff_degree_pos.mp (natDegree_pos_of_aeval_root hp hz inj)
 #align polynomial.degree_pos_of_aeval_root Polynomial.degree_pos_of_aeval_root
+-/
 
 #print Polynomial.modByMonic_eq_of_dvd_sub /-
 theorem modByMonic_eq_of_dvd_sub (hq : q.Monic) {p₁ p₂ : R[X]} (h : q ∣ p₁ - p₂) :
@@ -124,12 +128,14 @@ section
 
 variable [Ring S]
 
+#print Polynomial.aeval_modByMonic_eq_self_of_root /-
 theorem aeval_modByMonic_eq_self_of_root [Algebra R S] {p q : R[X]} (hq : q.Monic) {x : S}
     (hx : aeval x q = 0) : aeval x (p %ₘ q) = aeval x p :=
   by-- `eval₂_mod_by_monic_eq_self_of_root` doesn't work here as it needs commutativity
   rw [mod_by_monic_eq_sub_mul_div p hq, _root_.map_sub, _root_.map_mul, hx, MulZeroClass.zero_mul,
     sub_zero]
 #align polynomial.aeval_mod_by_monic_eq_self_of_root Polynomial.aeval_modByMonic_eq_self_of_root
+-/
 
 end
 
@@ -146,12 +152,15 @@ instance : NoZeroDivisors R[X]
     refine' eq_zero_or_eq_zero_of_mul_eq_zero _
     rw [← leading_coeff_zero, ← leading_coeff_mul, h]
 
+#print Polynomial.natDegree_mul /-
 theorem natDegree_mul (hp : p ≠ 0) (hq : q ≠ 0) : natDegree (p * q) = natDegree p + natDegree q :=
   by
   rw [← WithBot.coe_eq_coe, ← degree_eq_nat_degree (mul_ne_zero hp hq), WithBot.coe_add, ←
     degree_eq_nat_degree hp, ← degree_eq_nat_degree hq, degree_mul]
 #align polynomial.nat_degree_mul Polynomial.natDegree_mul
+-/
 
+#print Polynomial.trailingDegree_mul /-
 theorem trailingDegree_mul : (p * q).trailingDegree = p.trailingDegree + q.trailingDegree :=
   by
   by_cases hp : p = 0
@@ -162,7 +171,9 @@ theorem trailingDegree_mul : (p * q).trailingDegree = p.trailingDegree + q.trail
     trailing_degree_eq_nat_trailing_degree (mul_ne_zero hp hq), nat_trailing_degree_mul hp hq,
     WithTop.coe_add]
 #align polynomial.trailing_degree_mul Polynomial.trailingDegree_mul
+-/
 
+#print Polynomial.natDegree_pow /-
 @[simp]
 theorem natDegree_pow (p : R[X]) (n : ℕ) : natDegree (p ^ n) = n * natDegree p :=
   if hp0 : p = 0 then
@@ -172,50 +183,66 @@ theorem natDegree_pow (p : R[X]) (n : ℕ) : natDegree (p ^ n) = n * natDegree p
     natDegree_pow'
       (by rw [← leading_coeff_pow, Ne.def, leading_coeff_eq_zero] <;> exact pow_ne_zero _ hp0)
 #align polynomial.nat_degree_pow Polynomial.natDegree_pow
+-/
 
+#print Polynomial.degree_le_mul_left /-
 theorem degree_le_mul_left (p : R[X]) (hq : q ≠ 0) : degree p ≤ degree (p * q) :=
   if hp : p = 0 then by simp only [hp, MulZeroClass.zero_mul, le_refl]
   else by
     rw [degree_mul, degree_eq_nat_degree hp, degree_eq_nat_degree hq] <;>
       exact WithBot.coe_le_coe.2 (Nat.le_add_right _ _)
 #align polynomial.degree_le_mul_left Polynomial.degree_le_mul_left
+-/
 
+#print Polynomial.natDegree_le_of_dvd /-
 theorem natDegree_le_of_dvd {p q : R[X]} (h1 : p ∣ q) (h2 : q ≠ 0) : p.natDegree ≤ q.natDegree :=
   by
   rcases h1 with ⟨q, rfl⟩; rw [mul_ne_zero_iff] at h2 
   rw [nat_degree_mul h2.1 h2.2]; exact Nat.le_add_right _ _
 #align polynomial.nat_degree_le_of_dvd Polynomial.natDegree_le_of_dvd
+-/
 
+#print Polynomial.degree_le_of_dvd /-
 theorem degree_le_of_dvd {p q : R[X]} (h1 : p ∣ q) (h2 : q ≠ 0) : degree p ≤ degree q :=
   by
   rcases h1 with ⟨q, rfl⟩; rw [mul_ne_zero_iff] at h2 
   exact degree_le_mul_left p h2.2
 #align polynomial.degree_le_of_dvd Polynomial.degree_le_of_dvd
+-/
 
+#print Polynomial.eq_zero_of_dvd_of_degree_lt /-
 theorem eq_zero_of_dvd_of_degree_lt {p q : R[X]} (h₁ : p ∣ q) (h₂ : degree q < degree p) : q = 0 :=
   by
   by_contra hc
   exact (lt_iff_not_ge _ _).mp h₂ (degree_le_of_dvd h₁ hc)
 #align polynomial.eq_zero_of_dvd_of_degree_lt Polynomial.eq_zero_of_dvd_of_degree_lt
+-/
 
+#print Polynomial.eq_zero_of_dvd_of_natDegree_lt /-
 theorem eq_zero_of_dvd_of_natDegree_lt {p q : R[X]} (h₁ : p ∣ q) (h₂ : natDegree q < natDegree p) :
     q = 0 := by
   by_contra hc
   exact (lt_iff_not_ge _ _).mp h₂ (nat_degree_le_of_dvd h₁ hc)
 #align polynomial.eq_zero_of_dvd_of_nat_degree_lt Polynomial.eq_zero_of_dvd_of_natDegree_lt
+-/
 
+#print Polynomial.not_dvd_of_degree_lt /-
 theorem not_dvd_of_degree_lt {p q : R[X]} (h0 : q ≠ 0) (hl : q.degree < p.degree) : ¬p ∣ q :=
   by
   by_contra hcontra
   exact h0 (eq_zero_of_dvd_of_degree_lt hcontra hl)
 #align polynomial.not_dvd_of_degree_lt Polynomial.not_dvd_of_degree_lt
+-/
 
+#print Polynomial.not_dvd_of_natDegree_lt /-
 theorem not_dvd_of_natDegree_lt {p q : R[X]} (h0 : q ≠ 0) (hl : q.natDegree < p.natDegree) :
     ¬p ∣ q := by
   by_contra hcontra
   exact h0 (eq_zero_of_dvd_of_nat_degree_lt hcontra hl)
 #align polynomial.not_dvd_of_nat_degree_lt Polynomial.not_dvd_of_natDegree_lt
+-/
 
+#print Polynomial.natDegree_sub_eq_of_prod_eq /-
 /-- This lemma is useful for working with the `int_degree` of a rational function. -/
 theorem natDegree_sub_eq_of_prod_eq {p₁ p₂ q₁ q₂ : R[X]} (hp₁ : p₁ ≠ 0) (hq₁ : q₁ ≠ 0)
     (hp₂ : p₂ ≠ 0) (hq₂ : q₂ ≠ 0) (h_eq : p₁ * q₂ = p₂ * q₁) :
@@ -225,7 +252,9 @@ theorem natDegree_sub_eq_of_prod_eq {p₁ p₂ q₁ q₂ : R[X]} (hp₁ : p₁ 
   norm_cast
   rw [← nat_degree_mul hp₁ hq₂, ← nat_degree_mul hp₂ hq₁, h_eq]
 #align polynomial.nat_degree_sub_eq_of_prod_eq Polynomial.natDegree_sub_eq_of_prod_eq
+-/
 
+#print Polynomial.natDegree_eq_zero_of_isUnit /-
 theorem natDegree_eq_zero_of_isUnit (h : IsUnit p) : natDegree p = 0 :=
   by
   nontriviality R
@@ -234,17 +263,23 @@ theorem natDegree_eq_zero_of_isUnit (h : IsUnit p) : natDegree p = 0 :=
   rw [hq, nat_degree_one, eq_comm, add_eq_zero_iff] at this 
   exact this.1
 #align polynomial.nat_degree_eq_zero_of_is_unit Polynomial.natDegree_eq_zero_of_isUnit
+-/
 
+#print Polynomial.degree_eq_zero_of_isUnit /-
 theorem degree_eq_zero_of_isUnit [Nontrivial R] (h : IsUnit p) : degree p = 0 :=
   (natDegree_eq_zero_iff_degree_le_zero.mp <| natDegree_eq_zero_of_isUnit h).antisymm
     (zero_le_degree_iff.mpr h.NeZero)
 #align polynomial.degree_eq_zero_of_is_unit Polynomial.degree_eq_zero_of_isUnit
+-/
 
+#print Polynomial.degree_coe_units /-
 @[simp]
 theorem degree_coe_units [Nontrivial R] (u : R[X]ˣ) : degree (u : R[X]) = 0 :=
   degree_eq_zero_of_isUnit ⟨u, rfl⟩
 #align polynomial.degree_coe_units Polynomial.degree_coe_units
+-/
 
+#print Polynomial.isUnit_iff /-
 theorem isUnit_iff : IsUnit p ↔ ∃ r : R, IsUnit r ∧ C r = p :=
   ⟨fun hp =>
     ⟨p.coeff 0,
@@ -252,6 +287,7 @@ theorem isUnit_iff : IsUnit p ↔ ∃ r : R, IsUnit r ∧ C r = p :=
       ⟨isUnit_C.1 (h ▸ hp), h.symm⟩⟩,
     fun ⟨r, hr, hrp⟩ => hrp ▸ isUnit_C.2 hr⟩
 #align polynomial.is_unit_iff Polynomial.isUnit_iff
+-/
 
 variable [CharZero R]
 
@@ -293,6 +329,7 @@ section NoZeroDivisors
 
 variable [CommSemiring R] [NoZeroDivisors R] {p q : R[X]}
 
+#print Polynomial.irreducible_of_monic /-
 theorem irreducible_of_monic (hp : p.Monic) (hp1 : p ≠ 1) :
     Irreducible p ↔ ∀ f g : R[X], f.Monic → g.Monic → f * g = p → f = 1 ∨ g = 1 :=
   by
@@ -307,7 +344,9 @@ theorem irreducible_of_monic (hp : p.Monic) (hp1 : p ≠ 1) :
     rw [mul_mul_mul_comm, ← C_mul, ← leading_coeff_mul, ← hfg, hp.leading_coeff, C_1, mul_one,
       mul_comm, ← hfg]
 #align polynomial.irreducible_of_monic Polynomial.irreducible_of_monic
+-/
 
+#print Polynomial.Monic.irreducible_iff_natDegree /-
 theorem Monic.irreducible_iff_natDegree (hp : p.Monic) :
     Irreducible p ↔
       p ≠ 1 ∧ ∀ f g : R[X], f.Monic → g.Monic → f * g = p → f.natDegree = 0 ∨ g.natDegree = 0 :=
@@ -317,7 +356,9 @@ theorem Monic.irreducible_iff_natDegree (hp : p.Monic) :
   refine' forall₄_congr fun a b ha hb => _
   rw [ha.nat_degree_eq_zero_iff_eq_one, hb.nat_degree_eq_zero_iff_eq_one]
 #align polynomial.monic.irreducible_iff_nat_degree Polynomial.Monic.irreducible_iff_natDegree
+-/
 
+#print Polynomial.Monic.irreducible_iff_natDegree' /-
 theorem Monic.irreducible_iff_natDegree' (hp : p.Monic) :
     Irreducible p ↔
       p ≠ 1 ∧ ∀ f g : R[X], f.Monic → g.Monic → f * g = p → g.natDegree ∉ Ioc 0 (p.natDegree / 2) :=
@@ -333,7 +374,9 @@ theorem Monic.irreducible_iff_natDegree' (hp : p.Monic) :
     · exact ⟨g, f, hg, hf, mul_comm g f, h.1, add_le_add_left hl _⟩
     · exact ⟨f, g, hf, hg, rfl, h.2, add_le_add_right hl _⟩
 #align polynomial.monic.irreducible_iff_nat_degree' Polynomial.Monic.irreducible_iff_natDegree'
+-/
 
+#print Polynomial.Monic.not_irreducible_iff_exists_add_mul_eq_coeff /-
 theorem Monic.not_irreducible_iff_exists_add_mul_eq_coeff (hm : p.Monic) (hnd : p.natDegree = 2) :
     ¬Irreducible p ↔ ∃ c₁ c₂, p.coeff 0 = c₁ * c₂ ∧ p.coeff 1 = c₁ + c₂ :=
   by
@@ -353,14 +396,19 @@ theorem Monic.not_irreducible_iff_exists_add_mul_eq_coeff (hm : p.Monic) (hnd :
     ring
   · rintro rfl; simpa only [nat_degree_one] using hnd
 #align polynomial.monic.not_irreducible_iff_exists_add_mul_eq_coeff Polynomial.Monic.not_irreducible_iff_exists_add_mul_eq_coeff
+-/
 
+#print Polynomial.root_mul /-
 theorem root_mul : IsRoot (p * q) a ↔ IsRoot p a ∨ IsRoot q a := by
   simp_rw [is_root, eval_mul, mul_eq_zero]
 #align polynomial.root_mul Polynomial.root_mul
+-/
 
+#print Polynomial.root_or_root_of_root_mul /-
 theorem root_or_root_of_root_mul (h : IsRoot (p * q) a) : IsRoot p a ∨ IsRoot q a :=
   root_mul.1 h
 #align polynomial.root_or_root_of_root_mul Polynomial.root_or_root_of_root_mul
+-/
 
 end NoZeroDivisors
 
@@ -377,6 +425,7 @@ section CommRing
 
 variable [CommRing R]
 
+#print Polynomial.le_rootMultiplicity_iff /-
 /-- The multiplicity of `a` as root of a nonzero polynomial `p` is at least `n` iff
   `(X - a) ^ n` divides `p`. -/
 theorem le_rootMultiplicity_iff {p : R[X]} (p0 : p ≠ 0) {a : R} {n : ℕ} :
@@ -386,16 +435,22 @@ theorem le_rootMultiplicity_iff {p : R[X]} (p0 : p ≠ 0) {a : R} {n : ℕ} :
   refine' ⟨fun h => _, fun h m hm => (pow_dvd_pow _ hm).trans h⟩
   cases n; · rw [pow_zero]; apply one_dvd; · exact h n n.lt_succ_self
 #align polynomial.le_root_multiplicity_iff Polynomial.le_rootMultiplicity_iff
+-/
 
+#print Polynomial.rootMultiplicity_le_iff /-
 theorem rootMultiplicity_le_iff {p : R[X]} (p0 : p ≠ 0) (a : R) (n : ℕ) :
     rootMultiplicity a p ≤ n ↔ ¬(X - C a) ^ (n + 1) ∣ p := by
   rw [← (le_root_multiplicity_iff p0).Not, not_le, Nat.lt_add_one_iff]
 #align polynomial.root_multiplicity_le_iff Polynomial.rootMultiplicity_le_iff
+-/
 
+#print Polynomial.pow_rootMultiplicity_not_dvd /-
 theorem pow_rootMultiplicity_not_dvd {p : R[X]} (p0 : p ≠ 0) (a : R) :
     ¬(X - C a) ^ (rootMultiplicity a p + 1) ∣ p := by rw [← root_multiplicity_le_iff p0]
 #align polynomial.pow_root_multiplicity_not_dvd Polynomial.pow_rootMultiplicity_not_dvd
+-/
 
+#print Polynomial.rootMultiplicity_add /-
 /-- The multiplicity of `p + q` is at least the minimum of the multiplicities. -/
 theorem rootMultiplicity_add {p q : R[X]} (a : R) (hzero : p + q ≠ 0) :
     min (rootMultiplicity a p) (rootMultiplicity a q) ≤ rootMultiplicity a (p + q) :=
@@ -405,6 +460,7 @@ theorem rootMultiplicity_add {p q : R[X]} (a : R) (hzero : p + q ≠ 0) :
   have hdivq : (X - C a) ^ root_multiplicity a q ∣ q := pow_root_multiplicity_dvd q a
   exact min_pow_dvd_add hdivp hdivq
 #align polynomial.root_multiplicity_add Polynomial.rootMultiplicity_add
+-/
 
 variable [IsDomain R] {p q : R[X]}
 
@@ -412,10 +468,12 @@ section Roots
 
 open Multiset
 
+#print Polynomial.prime_X_sub_C /-
 theorem prime_X_sub_C (r : R) : Prime (X - C r) :=
   ⟨X_sub_C_ne_zero r, not_isUnit_X_sub_C r, fun _ _ => by
     simp_rw [dvd_iff_is_root, is_root.def, eval_mul, mul_eq_zero]; exact id⟩
 #align polynomial.prime_X_sub_C Polynomial.prime_X_sub_C
+-/
 
 #print Polynomial.prime_X /-
 theorem prime_X : Prime (X : R[X]) := by convert prime_X_sub_C (0 : R); simp
@@ -429,18 +487,25 @@ theorem Monic.prime_of_degree_eq_one (hp1 : degree p = 1) (hm : Monic p) : Prime
 #align polynomial.monic.prime_of_degree_eq_one Polynomial.Monic.prime_of_degree_eq_one
 -/
 
+#print Polynomial.irreducible_X_sub_C /-
 theorem irreducible_X_sub_C (r : R) : Irreducible (X - C r) :=
   (prime_X_sub_C r).Irreducible
 #align polynomial.irreducible_X_sub_C Polynomial.irreducible_X_sub_C
+-/
 
+#print Polynomial.irreducible_X /-
 theorem irreducible_X : Irreducible (X : R[X]) :=
   Prime.irreducible prime_X
 #align polynomial.irreducible_X Polynomial.irreducible_X
+-/
 
+#print Polynomial.Monic.irreducible_of_degree_eq_one /-
 theorem Monic.irreducible_of_degree_eq_one (hp1 : degree p = 1) (hm : Monic p) : Irreducible p :=
   (hm.prime_of_degree_eq_one hp1).Irreducible
 #align polynomial.monic.irreducible_of_degree_eq_one Polynomial.Monic.irreducible_of_degree_eq_one
+-/
 
+#print Polynomial.eq_of_monic_of_associated /-
 theorem eq_of_monic_of_associated (hp : p.Monic) (hq : q.Monic) (hpq : Associated p q) : p = q :=
   by
   obtain ⟨u, hu⟩ := hpq
@@ -450,6 +515,7 @@ theorem eq_of_monic_of_associated (hp : p.Monic) (hq : q.Monic) (hpq : Associate
   rwa [hq, C_1, mul_one] at hu 
   all_goals infer_instance
 #align polynomial.eq_of_monic_of_associated Polynomial.eq_of_monic_of_associated
+-/
 
 #print Polynomial.rootMultiplicity_mul /-
 theorem rootMultiplicity_mul {p q : R[X]} {x : R} (hpq : p * q ≠ 0) :
@@ -463,11 +529,14 @@ theorem rootMultiplicity_mul {p q : R[X]} {x : R} (hpq : p * q ≠ 0) :
 #align polynomial.root_multiplicity_mul Polynomial.rootMultiplicity_mul
 -/
 
+#print Polynomial.rootMultiplicity_X_sub_C_self /-
 theorem rootMultiplicity_X_sub_C_self {x : R} : rootMultiplicity x (X - C x) = 1 := by
   rw [root_multiplicity_eq_multiplicity, dif_neg (X_sub_C_ne_zero x),
     multiplicity.get_multiplicity_self]
 #align polynomial.root_multiplicity_X_sub_C_self Polynomial.rootMultiplicity_X_sub_C_self
+-/
 
+#print Polynomial.rootMultiplicity_X_sub_C /-
 theorem rootMultiplicity_X_sub_C {x y : R} :
     rootMultiplicity x (X - C y) = if x = y then 1 else 0 :=
   by
@@ -476,7 +545,9 @@ theorem rootMultiplicity_X_sub_C {x y : R} :
     exact root_multiplicity_X_sub_C_self
   exact root_multiplicity_eq_zero (mt root_X_sub_C.mp (Ne.symm hxy))
 #align polynomial.root_multiplicity_X_sub_C Polynomial.rootMultiplicity_X_sub_C
+-/
 
+#print Polynomial.rootMultiplicity_X_sub_C_pow /-
 /-- The multiplicity of `a` as root of `(X - a) ^ n` is `n`. -/
 theorem rootMultiplicity_X_sub_C_pow (a : R) (n : ℕ) : rootMultiplicity a ((X - C a) ^ n) = n :=
   by
@@ -487,7 +558,9 @@ theorem rootMultiplicity_X_sub_C_pow (a : R) (n : ℕ) : rootMultiplicity a ((X
   rw [pow_succ (X - C a) n] at hzero ⊢
   simp only [root_multiplicity_mul hzero, root_multiplicity_X_sub_C_self, hn, Nat.one_add]
 #align polynomial.root_multiplicity_X_sub_C_pow Polynomial.rootMultiplicity_X_sub_C_pow
+-/
 
+#print Polynomial.exists_multiset_roots /-
 theorem exists_multiset_roots :
     ∀ {p : R[X]} (hp : p ≠ 0),
       ∃ s : Multiset R, (s.card : WithBot ℕ) ≤ degree p ∧ ∀ a, s.count a = rootMultiplicity a p
@@ -527,6 +600,7 @@ theorem exists_multiset_roots :
       ⟨0, (degree_eq_nat_degree hp).symm ▸ WithBot.coe_le_coe.2 (Nat.zero_le _), by intro a;
         rw [count_zero, root_multiplicity_eq_zero (not_exists.mp h a)]⟩
 #align polynomial.exists_multiset_roots Polynomial.exists_multiset_roots
+-/
 
 #print Polynomial.roots /-
 /-- `roots p` noncomputably gives a multiset containing all the roots of `p`,
@@ -543,20 +617,25 @@ theorem roots_zero : (0 : R[X]).roots = 0 :=
 #align polynomial.roots_zero Polynomial.roots_zero
 -/
 
+#print Polynomial.card_roots /-
 theorem card_roots (hp0 : p ≠ 0) : ((roots p).card : WithBot ℕ) ≤ degree p :=
   by
   unfold roots
   rw [dif_neg hp0]
   exact (Classical.choose_spec (exists_multiset_roots hp0)).1
 #align polynomial.card_roots Polynomial.card_roots
+-/
 
+#print Polynomial.card_roots' /-
 theorem card_roots' (p : R[X]) : p.roots.card ≤ natDegree p :=
   by
   by_cases hp0 : p = 0
   · simp [hp0]
   exact WithBot.coe_le_coe.1 (le_trans (card_roots hp0) (le_of_eq <| degree_eq_nat_degree hp0))
 #align polynomial.card_roots' Polynomial.card_roots'
+-/
 
+#print Polynomial.card_roots_sub_C /-
 theorem card_roots_sub_C {p : R[X]} {a : R} (hp0 : 0 < degree p) :
     ((p - C a).roots.card : WithBot ℕ) ≤ degree p :=
   calc
@@ -564,13 +643,16 @@ theorem card_roots_sub_C {p : R[X]} {a : R} (hp0 : 0 < degree p) :
       card_roots <| mt sub_eq_zero.1 fun h => not_le_of_gt hp0 <| h.symm ▸ degree_C_le
     _ = degree p := by rw [sub_eq_add_neg, ← C_neg] <;> exact degree_add_C hp0
 #align polynomial.card_roots_sub_C Polynomial.card_roots_sub_C
+-/
 
+#print Polynomial.card_roots_sub_C' /-
 theorem card_roots_sub_C' {p : R[X]} {a : R} (hp0 : 0 < degree p) :
     (p - C a).roots.card ≤ natDegree p :=
   WithBot.coe_le_coe.1
     (le_trans (card_roots_sub_C hp0)
       (le_of_eq <| degree_eq_natDegree fun h => by simp_all [lt_irrefl]))
 #align polynomial.card_roots_sub_C' Polynomial.card_roots_sub_C'
+-/
 
 #print Polynomial.count_roots /-
 @[simp]
@@ -655,32 +737,43 @@ theorem roots_mul {p q : R[X]} (hpq : p * q ≠ 0) : (p * q).roots = p.roots + q
 #align polynomial.roots_mul Polynomial.roots_mul
 -/
 
+#print Polynomial.roots.le_of_dvd /-
 theorem roots.le_of_dvd (h : q ≠ 0) : p ∣ q → roots p ≤ roots q :=
   by
   rintro ⟨k, rfl⟩
   exact multiset.le_iff_exists_add.mpr ⟨k.roots, roots_mul h⟩
 #align polynomial.roots.le_of_dvd Polynomial.roots.le_of_dvd
+-/
 
+#print Polynomial.mem_roots_sub_C' /-
 theorem mem_roots_sub_C' {p : R[X]} {a x : R} : x ∈ (p - C a).roots ↔ p ≠ C a ∧ p.eval x = a := by
   rw [mem_roots', is_root.def, sub_ne_zero, eval_sub, sub_eq_zero, eval_C]
 #align polynomial.mem_roots_sub_C' Polynomial.mem_roots_sub_C'
+-/
 
+#print Polynomial.mem_roots_sub_C /-
 theorem mem_roots_sub_C {p : R[X]} {a x : R} (hp0 : 0 < degree p) :
     x ∈ (p - C a).roots ↔ p.eval x = a :=
   mem_roots_sub_C'.trans <| and_iff_right fun hp => hp0.not_le <| hp.symm ▸ degree_C_le
 #align polynomial.mem_roots_sub_C Polynomial.mem_roots_sub_C
+-/
 
+#print Polynomial.roots_X_sub_C /-
 @[simp]
 theorem roots_X_sub_C (r : R) : roots (X - C r) = {r} :=
   by
   ext s
   rw [count_roots, root_multiplicity_X_sub_C, count_singleton]
 #align polynomial.roots_X_sub_C Polynomial.roots_X_sub_C
+-/
 
+#print Polynomial.roots_X /-
 @[simp]
 theorem roots_X : roots (X : R[X]) = {0} := by rw [← roots_X_sub_C, C_0, sub_zero]
 #align polynomial.roots_X Polynomial.roots_X
+-/
 
+#print Polynomial.roots_C /-
 @[simp]
 theorem roots_C (x : R) : (C x).roots = 0 :=
   if H : x = 0 then by rw [H, C_0, roots_zero]
@@ -688,6 +781,7 @@ theorem roots_C (x : R) : (C x).roots = 0 :=
     Multiset.ext.mpr fun r => by
       rw [count_roots, count_zero, root_multiplicity_eq_zero (not_is_root_C _ _ H)]
 #align polynomial.roots_C Polynomial.roots_C
+-/
 
 #print Polynomial.roots_one /-
 @[simp]
@@ -696,17 +790,21 @@ theorem roots_one : (1 : R[X]).roots = ∅ :=
 #align polynomial.roots_one Polynomial.roots_one
 -/
 
+#print Polynomial.roots_C_mul /-
 @[simp]
 theorem roots_C_mul (p : R[X]) (ha : a ≠ 0) : (C a * p).roots = p.roots := by
   by_cases hp : p = 0 <;>
     simp only [roots_mul, *, Ne.def, mul_eq_zero, C_eq_zero, or_self_iff, not_false_iff, roots_C,
       zero_add, MulZeroClass.mul_zero]
 #align polynomial.roots_C_mul Polynomial.roots_C_mul
+-/
 
+#print Polynomial.roots_smul_nonzero /-
 @[simp]
 theorem roots_smul_nonzero (p : R[X]) (ha : a ≠ 0) : (a • p).roots = p.roots := by
   rw [smul_eq_C_mul, roots_C_mul _ ha]
 #align polynomial.roots_smul_nonzero Polynomial.roots_smul_nonzero
+-/
 
 #print Polynomial.roots_list_prod /-
 theorem roots_list_prod (L : List R[X]) :
@@ -725,13 +823,16 @@ theorem roots_multiset_prod (m : Multiset R[X]) : (0 : R[X]) ∉ m → m.Prod.ro
 #align polynomial.roots_multiset_prod Polynomial.roots_multiset_prod
 -/
 
+#print Polynomial.roots_prod /-
 theorem roots_prod {ι : Type _} (f : ι → R[X]) (s : Finset ι) :
     s.Prod f ≠ 0 → (s.Prod f).roots = s.val.bind fun i => roots (f i) :=
   by
   rcases s with ⟨m, hm⟩
   simpa [Multiset.prod_eq_zero_iff, bind_map] using roots_multiset_prod (m.map f)
 #align polynomial.roots_prod Polynomial.roots_prod
+-/
 
+#print Polynomial.roots_pow /-
 @[simp]
 theorem roots_pow (p : R[X]) (n : ℕ) : (p ^ n).roots = n • p.roots :=
   by
@@ -743,24 +844,34 @@ theorem roots_pow (p : R[X]) (n : ℕ) : (p ^ n).roots = n • p.roots :=
       rw [pow_succ', roots_mul (mul_ne_zero (pow_ne_zero _ hp) hp), ihn, Nat.succ_eq_add_one,
         add_smul, one_smul]
 #align polynomial.roots_pow Polynomial.roots_pow
+-/
 
+#print Polynomial.roots_X_pow /-
 theorem roots_X_pow (n : ℕ) : (X ^ n : R[X]).roots = n • {0} := by rw [roots_pow, roots_X]
 #align polynomial.roots_X_pow Polynomial.roots_X_pow
+-/
 
+#print Polynomial.roots_C_mul_X_pow /-
 theorem roots_C_mul_X_pow (ha : a ≠ 0) (n : ℕ) : (C a * X ^ n).roots = n • {0} := by
   rw [roots_C_mul _ ha, roots_X_pow]
 #align polynomial.roots_C_mul_X_pow Polynomial.roots_C_mul_X_pow
+-/
 
+#print Polynomial.roots_monomial /-
 @[simp]
 theorem roots_monomial (ha : a ≠ 0) (n : ℕ) : (monomial n a).roots = n • {0} := by
   rw [← C_mul_X_pow_eq_monomial, roots_C_mul_X_pow ha]
 #align polynomial.roots_monomial Polynomial.roots_monomial
+-/
 
+#print Polynomial.roots_prod_X_sub_C /-
 theorem roots_prod_X_sub_C (s : Finset R) : (s.Prod fun a => X - C a).roots = s.val :=
   (roots_prod (fun a => X - C a) s (prod_ne_zero_iff.mpr fun a _ => X_sub_C_ne_zero a)).trans
     (by simp_rw [roots_X_sub_C, Multiset.bind_singleton, Multiset.map_id'])
 #align polynomial.roots_prod_X_sub_C Polynomial.roots_prod_X_sub_C
+-/
 
+#print Polynomial.roots_multiset_prod_X_sub_C /-
 @[simp]
 theorem roots_multiset_prod_X_sub_C (s : Multiset R) : (s.map fun a => X - C a).Prod.roots = s :=
   by
@@ -768,7 +879,9 @@ theorem roots_multiset_prod_X_sub_C (s : Multiset R) : (s.map fun a => X - C a).
   · simp_rw [roots_X_sub_C, Multiset.bind_singleton, Multiset.map_id']
   · rw [Multiset.mem_map]; rintro ⟨a, -, h⟩; exact X_sub_C_ne_zero a h
 #align polynomial.roots_multiset_prod_X_sub_C Polynomial.roots_multiset_prod_X_sub_C
+-/
 
+#print Polynomial.natDegree_multiset_prod_X_sub_C_eq_card /-
 @[simp]
 theorem natDegree_multiset_prod_X_sub_C_eq_card (s : Multiset R) :
     (s.map fun a => X - C a).Prod.natDegree = s.card :=
@@ -779,7 +892,9 @@ theorem natDegree_multiset_prod_X_sub_C_eq_card (s : Multiset R) :
       mul_one]
   · exact Multiset.forall_mem_map_iff.2 fun a _ => monic_X_sub_C a
 #align polynomial.nat_degree_multiset_prod_X_sub_C_eq_card Polynomial.natDegree_multiset_prod_X_sub_C_eq_card
+-/
 
+#print Polynomial.card_roots_X_pow_sub_C /-
 theorem card_roots_X_pow_sub_C {n : ℕ} (hn : 0 < n) (a : R) :
     (roots ((X : R[X]) ^ n - C a)).card ≤ n :=
   WithBot.coe_le_coe.1 <|
@@ -788,6 +903,7 @@ theorem card_roots_X_pow_sub_C {n : ℕ} (hn : 0 < n) (a : R) :
         card_roots (X_pow_sub_C_ne_zero hn a)
       _ = n := degree_X_pow_sub_C hn a
 #align polynomial.card_roots_X_pow_sub_C Polynomial.card_roots_X_pow_sub_C
+-/
 
 section NthRoots
 
@@ -798,11 +914,13 @@ def nthRoots (n : ℕ) (a : R) : Multiset R :=
 #align polynomial.nth_roots Polynomial.nthRoots
 -/
 
+#print Polynomial.mem_nthRoots /-
 @[simp]
 theorem mem_nthRoots {n : ℕ} (hn : 0 < n) {a x : R} : x ∈ nthRoots n a ↔ x ^ n = a := by
   rw [nth_roots, mem_roots (X_pow_sub_C_ne_zero hn a), is_root.def, eval_sub, eval_C, eval_pow,
     eval_X, sub_eq_zero]
 #align polynomial.mem_nth_roots Polynomial.mem_nthRoots
+-/
 
 #print Polynomial.nthRoots_zero /-
 @[simp]
@@ -811,6 +929,7 @@ theorem nthRoots_zero (r : R) : nthRoots 0 r = 0 := by
 #align polynomial.nth_roots_zero Polynomial.nthRoots_zero
 -/
 
+#print Polynomial.card_nthRoots /-
 theorem card_nthRoots (n : ℕ) (a : R) : (nthRoots n a).card ≤ n :=
   if hn : n = 0 then
     if h : (X : R[X]) ^ n - C a = 0 then by
@@ -825,12 +944,15 @@ theorem card_nthRoots (n : ℕ) (a : R) : (nthRoots n a).card ≤ n :=
     rw [← WithBot.coe_le_coe, ← degree_X_pow_sub_C (Nat.pos_of_ne_zero hn) a] <;>
       exact card_roots (X_pow_sub_C_ne_zero (Nat.pos_of_ne_zero hn) a)
 #align polynomial.card_nth_roots Polynomial.card_nthRoots
+-/
 
+#print Polynomial.nthRoots_two_eq_zero_iff /-
 @[simp]
 theorem nthRoots_two_eq_zero_iff {r : R} : nthRoots 2 r = 0 ↔ ¬IsSquare r := by
   simp_rw [isSquare_iff_exists_sq, eq_zero_iff_forall_not_mem, mem_nth_roots (by norm_num : 0 < 2),
     ← not_exists, eq_comm]
 #align polynomial.nth_roots_two_eq_zero_iff Polynomial.nthRoots_two_eq_zero_iff
+-/
 
 #print Polynomial.nthRootsFinset /-
 /-- The multiset `nth_roots ↑n (1 : R)` as a finset. -/
@@ -839,10 +961,12 @@ def nthRootsFinset (n : ℕ) (R : Type _) [CommRing R] [IsDomain R] : Finset R :
 #align polynomial.nth_roots_finset Polynomial.nthRootsFinset
 -/
 
+#print Polynomial.mem_nthRootsFinset /-
 @[simp]
 theorem mem_nthRootsFinset {n : ℕ} (h : 0 < n) {x : R} : x ∈ nthRootsFinset n R ↔ x ^ (n : ℕ) = 1 :=
   by rw [nth_roots_finset, mem_to_finset, mem_nth_roots h]
 #align polynomial.mem_nth_roots_finset Polynomial.mem_nthRootsFinset
+-/
 
 #print Polynomial.nthRootsFinset_zero /-
 @[simp]
@@ -858,26 +982,35 @@ theorem Monic.comp (hp : p.Monic) (hq : q.Monic) (h : q.natDegree ≠ 0) : (p.co
 #align polynomial.monic.comp Polynomial.Monic.comp
 -/
 
+#print Polynomial.Monic.comp_X_add_C /-
 theorem Monic.comp_X_add_C (hp : p.Monic) (r : R) : (p.comp (X + C r)).Monic :=
   by
   refine' hp.comp (monic_X_add_C _) fun ha => _
   rw [nat_degree_X_add_C] at ha 
   exact one_ne_zero ha
 #align polynomial.monic.comp_X_add_C Polynomial.Monic.comp_X_add_C
+-/
 
+#print Polynomial.Monic.comp_X_sub_C /-
 theorem Monic.comp_X_sub_C (hp : p.Monic) (r : R) : (p.comp (X - C r)).Monic := by
   simpa using hp.comp_X_add_C (-r)
 #align polynomial.monic.comp_X_sub_C Polynomial.Monic.comp_X_sub_C
+-/
 
+#print Polynomial.units_coeff_zero_smul /-
 theorem units_coeff_zero_smul (c : R[X]ˣ) (p : R[X]) : (c : R[X]).coeff 0 • p = c * p := by
   rw [← Polynomial.C_mul', ← Polynomial.eq_C_of_degree_eq_zero (degree_coe_units c)]
 #align polynomial.units_coeff_zero_smul Polynomial.units_coeff_zero_smul
+-/
 
+#print Polynomial.natDegree_coe_units /-
 @[simp]
 theorem natDegree_coe_units (u : R[X]ˣ) : natDegree (u : R[X]) = 0 :=
   natDegree_eq_of_degree_eq_some (degree_coe_units u)
 #align polynomial.nat_degree_coe_units Polynomial.natDegree_coe_units
+-/
 
+#print Polynomial.comp_eq_zero_iff /-
 theorem comp_eq_zero_iff : p.comp q = 0 ↔ p = 0 ∨ p.eval (q.coeff 0) = 0 ∧ q = C (q.coeff 0) :=
   by
   constructor
@@ -894,13 +1027,16 @@ theorem comp_eq_zero_iff : p.comp q = 0 ↔ p = 0 ∨ p.eval (q.coeff 0) = 0 ∧
     exact fun h =>
       Or.ndrec (fun h => by rw [h, zero_comp]) (fun h => by rw [h.2, comp_C, h.1, C_0]) h
 #align polynomial.comp_eq_zero_iff Polynomial.comp_eq_zero_iff
+-/
 
+#print Polynomial.zero_of_eval_zero /-
 theorem zero_of_eval_zero [Infinite R] (p : R[X]) (h : ∀ x, p.eval x = 0) : p = 0 := by
   classical by_contra hp <;>
     exact
       Fintype.false
         ⟨p.roots.to_finset, fun x => multiset.mem_to_finset.mpr ((mem_roots hp).mpr (h _))⟩
 #align polynomial.zero_of_eval_zero Polynomial.zero_of_eval_zero
+-/
 
 #print Polynomial.funext /-
 theorem funext [Infinite R] {p q : R[X]} (ext : ∀ r : R, p.eval r = q.eval r) : p = q :=
@@ -924,20 +1060,26 @@ def rootSet (p : T[X]) (S) [CommRing S] [IsDomain S] [Algebra T S] : Set S :=
 #align polynomial.root_set Polynomial.rootSet
 -/
 
+#print Polynomial.rootSet_def /-
 theorem rootSet_def (p : T[X]) (S) [CommRing S] [IsDomain S] [Algebra T S] :
     p.rootSet S = (p.map (algebraMap T S)).roots.toFinset :=
   rfl
 #align polynomial.root_set_def Polynomial.rootSet_def
+-/
 
+#print Polynomial.rootSet_C /-
 @[simp]
 theorem rootSet_C [CommRing S] [IsDomain S] [Algebra T S] (a : T) : (C a).rootSet S = ∅ := by
   rw [root_set_def, map_C, roots_C, Multiset.toFinset_zero, Finset.coe_empty]
 #align polynomial.root_set_C Polynomial.rootSet_C
+-/
 
+#print Polynomial.rootSet_zero /-
 @[simp]
 theorem rootSet_zero (S) [CommRing S] [IsDomain S] [Algebra T S] : (0 : T[X]).rootSet S = ∅ := by
   rw [← C_0, root_set_C]
 #align polynomial.root_set_zero Polynomial.rootSet_zero
+-/
 
 #print Polynomial.rootSetFintype /-
 instance rootSetFintype (p : T[X]) (S : Type _) [CommRing S] [IsDomain S] [Algebra T S] :
@@ -946,11 +1088,14 @@ instance rootSetFintype (p : T[X]) (S : Type _) [CommRing S] [IsDomain S] [Algeb
 #align polynomial.root_set_fintype Polynomial.rootSetFintype
 -/
 
+#print Polynomial.rootSet_finite /-
 theorem rootSet_finite (p : T[X]) (S : Type _) [CommRing S] [IsDomain S] [Algebra T S] :
     (p.rootSet S).Finite :=
   Set.toFinite _
 #align polynomial.root_set_finite Polynomial.rootSet_finite
+-/
 
+#print Polynomial.bUnion_roots_finite /-
 /-- The set of roots of all polynomials of bounded degree and having coefficients in a finite set
 is finite. -/
 theorem bUnion_roots_finite {R S : Type _} [Semiring R] [CommRing S] [IsDomain S] (m : R →+* S)
@@ -968,24 +1113,32 @@ theorem bUnion_roots_finite {R S : Type _} [Semiring R] [CommRing S] [IsDomain S
         exact id congr_fun hxy ⟨i, Nat.lt_succ_of_le hi⟩)
     fun i hi => Finset.finite_toSet _
 #align polynomial.bUnion_roots_finite Polynomial.bUnion_roots_finite
+-/
 
+#print Polynomial.mem_rootSet' /-
 theorem mem_rootSet' {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Algebra T S] {a : S} :
     a ∈ p.rootSet S ↔ p.map (algebraMap T S) ≠ 0 ∧ aeval a p = 0 := by
   rw [root_set, Finset.mem_coe, mem_to_finset, mem_roots', is_root.def, ← eval₂_eq_eval_map,
     aeval_def]
 #align polynomial.mem_root_set' Polynomial.mem_rootSet'
+-/
 
+#print Polynomial.mem_rootSet /-
 theorem mem_rootSet {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Algebra T S]
     [NoZeroSMulDivisors T S] {a : S} : a ∈ p.rootSet S ↔ p ≠ 0 ∧ aeval a p = 0 := by
   rw [mem_root_set',
     (map_injective _ (NoZeroSMulDivisors.algebraMap_injective T S)).ne_iff' (Polynomial.map_zero _)]
 #align polynomial.mem_root_set Polynomial.mem_rootSet
+-/
 
+#print Polynomial.mem_rootSet_of_ne /-
 theorem mem_rootSet_of_ne {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Algebra T S]
     [NoZeroSMulDivisors T S] (hp : p ≠ 0) {a : S} : a ∈ p.rootSet S ↔ aeval a p = 0 :=
   mem_rootSet.trans <| and_iff_right hp
 #align polynomial.mem_root_set_of_ne Polynomial.mem_rootSet_of_ne
+-/
 
+#print Polynomial.rootSet_maps_to' /-
 theorem rootSet_maps_to' {p : T[X]} {S S'} [CommRing S] [IsDomain S] [Algebra T S] [CommRing S']
     [IsDomain S'] [Algebra T S'] (hp : p.map (algebraMap T S') = 0 → p.map (algebraMap T S) = 0)
     (f : S →ₐ[T] S') : (p.rootSet S).MapsTo f (p.rootSet S') := fun x hx =>
@@ -994,6 +1147,7 @@ theorem rootSet_maps_to' {p : T[X]} {S S'} [CommRing S] [IsDomain S] [Algebra T
   rw [aeval_alg_hom, AlgHom.comp_apply, hx.2, _root_.map_zero]
   exact ⟨mt hp hx.1, rfl⟩
 #align polynomial.root_set_maps_to' Polynomial.rootSet_maps_to'
+-/
 
 #print Polynomial.ne_zero_of_mem_rootSet /-
 theorem ne_zero_of_mem_rootSet {p : T[X]} [CommRing S] [IsDomain S] [Algebra T S] {a : S}
@@ -1001,11 +1155,14 @@ theorem ne_zero_of_mem_rootSet {p : T[X]} [CommRing S] [IsDomain S] [Algebra T S
 #align polynomial.ne_zero_of_mem_root_set Polynomial.ne_zero_of_mem_rootSet
 -/
 
+#print Polynomial.aeval_eq_zero_of_mem_rootSet /-
 theorem aeval_eq_zero_of_mem_rootSet {p : T[X]} [CommRing S] [IsDomain S] [Algebra T S] {a : S}
     (hx : a ∈ p.rootSet S) : aeval a p = 0 :=
   (mem_rootSet'.1 hx).2
 #align polynomial.aeval_eq_zero_of_mem_root_set Polynomial.aeval_eq_zero_of_mem_rootSet
+-/
 
+#print Polynomial.rootSet_mapsTo /-
 theorem rootSet_mapsTo {p : T[X]} {S S'} [CommRing S] [IsDomain S] [Algebra T S] [CommRing S']
     [IsDomain S'] [Algebra T S'] [NoZeroSMulDivisors T S'] (f : S →ₐ[T] S') :
     (p.rootSet S).MapsTo f (p.rootSet S') :=
@@ -1015,22 +1172,28 @@ theorem rootSet_mapsTo {p : T[X]} {S S'} [CommRing S] [IsDomain S] [Algebra T S]
     map_injective _ (NoZeroSMulDivisors.algebraMap_injective T S') (by rwa [Polynomial.map_zero])
   exact Polynomial.map_zero _
 #align polynomial.root_set_maps_to Polynomial.rootSet_mapsTo
+-/
 
 end Roots
 
+#print Polynomial.coeff_coe_units_zero_ne_zero /-
 theorem coeff_coe_units_zero_ne_zero (u : R[X]ˣ) : coeff (u : R[X]) 0 ≠ 0 :=
   by
   conv in 0 => rw [← nat_degree_coe_units u]
   rw [← leading_coeff, Ne.def, leading_coeff_eq_zero]
   exact Units.ne_zero _
 #align polynomial.coeff_coe_units_zero_ne_zero Polynomial.coeff_coe_units_zero_ne_zero
+-/
 
+#print Polynomial.degree_eq_degree_of_associated /-
 theorem degree_eq_degree_of_associated (h : Associated p q) : degree p = degree q :=
   by
   let ⟨u, hu⟩ := h
   simp [hu.symm]
 #align polynomial.degree_eq_degree_of_associated Polynomial.degree_eq_degree_of_associated
+-/
 
+#print Polynomial.degree_eq_one_of_irreducible_of_root /-
 theorem degree_eq_one_of_irreducible_of_root (hi : Irreducible p) {x : R} (hx : IsRoot p x) :
     degree p = 1 :=
   let ⟨g, hg⟩ := dvd_iff_isRoot.2 hx
@@ -1042,6 +1205,7 @@ theorem degree_eq_one_of_irreducible_of_root (hi : Irreducible p) {x : R} (hx :
       rw [h₁] at h₂  <;> exact absurd h₂ (by decide))
     fun hgu => by rw [hg, degree_mul, degree_X_sub_C, degree_eq_zero_of_is_unit hgu, add_zero]
 #align polynomial.degree_eq_one_of_irreducible_of_root Polynomial.degree_eq_one_of_irreducible_of_root
+-/
 
 #print Polynomial.leadingCoeff_divByMonic_of_monic /-
 /-- Division by a monic polynomial doesn't change the leading coefficient. -/
@@ -1059,6 +1223,7 @@ theorem leadingCoeff_divByMonic_of_monic {R : Type u} [CommRing R] {p q : R[X]}
 #align polynomial.leading_coeff_div_by_monic_of_monic Polynomial.leadingCoeff_divByMonic_of_monic
 -/
 
+#print Polynomial.leadingCoeff_divByMonic_X_sub_C /-
 theorem leadingCoeff_divByMonic_X_sub_C (p : R[X]) (hp : degree p ≠ 0) (a : R) :
     leadingCoeff (p /ₘ (X - C a)) = leadingCoeff p :=
   by
@@ -1068,7 +1233,9 @@ theorem leadingCoeff_divByMonic_X_sub_C (p : R[X]) (hp : degree p ≠ 0) (a : R)
   refine' leading_coeff_div_by_monic_of_monic (monic_X_sub_C a) _
   rwa [degree_X_sub_C, Nat.WithBot.one_le_iff_zero_lt]
 #align polynomial.leading_coeff_div_by_monic_X_sub_C Polynomial.leadingCoeff_divByMonic_X_sub_C
+-/
 
+#print Polynomial.eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le /-
 theorem eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le {R} [CommRing R] {p q : R[X]}
     (hp : p.Monic) (hdiv : p ∣ q) (hdeg : q.natDegree ≤ p.natDegree) : q = C q.leadingCoeff * p :=
   by
@@ -1081,6 +1248,7 @@ theorem eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le {R} [CommRing R] {p
   · convert hr; convert leading_coeff_C _ using 1; rw [hr, leading_coeff_mul_monic hp]
   · exact (add_right_inj _).1 (le_antisymm hdeg <| Nat.le.intro rfl)
 #align polynomial.eq_leading_coeff_mul_of_monic_of_dvd_of_nat_degree_le Polynomial.eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le
+-/
 
 #print Polynomial.eq_of_monic_of_dvd_of_natDegree_le /-
 theorem eq_of_monic_of_dvd_of_natDegree_le {R} [CommRing R] {p q : R[X]} (hp : p.Monic)
@@ -1091,6 +1259,7 @@ theorem eq_of_monic_of_dvd_of_natDegree_le {R} [CommRing R] {p q : R[X]} (hp : p
 #align polynomial.eq_of_monic_of_dvd_of_nat_degree_le Polynomial.eq_of_monic_of_dvd_of_natDegree_le
 -/
 
+#print Polynomial.isCoprime_X_sub_C_of_isUnit_sub /-
 theorem isCoprime_X_sub_C_of_isUnit_sub {R} [CommRing R] {a b : R} (h : IsUnit (a - b)) :
     IsCoprime (X - C a) (X - C b) :=
   ⟨-C h.Unit⁻¹.val, C h.Unit⁻¹.val,
@@ -1098,22 +1267,30 @@ theorem isCoprime_X_sub_C_of_isUnit_sub {R} [CommRing R] {a b : R} (h : IsUnit (
     rw [neg_mul_comm, ← left_distrib, neg_add_eq_sub, sub_sub_sub_cancel_left, ← C_sub, ← C_mul]
     convert C_1; exact h.coe_inv_mul⟩
 #align polynomial.is_coprime_X_sub_C_of_is_unit_sub Polynomial.isCoprime_X_sub_C_of_isUnit_sub
+-/
 
+#print Polynomial.pairwise_coprime_X_sub_C /-
 theorem pairwise_coprime_X_sub_C {K} [Field K] {I : Type v} {s : I → K} (H : Function.Injective s) :
     Pairwise (IsCoprime on fun i : I => X - C (s i)) := fun i j hij =>
   isCoprime_X_sub_C_of_isUnit_sub (sub_ne_zero_of_ne <| H.Ne hij).IsUnit
 #align polynomial.pairwise_coprime_X_sub_C Polynomial.pairwise_coprime_X_sub_C
+-/
 
+#print Polynomial.monic_prod_multiset_X_sub_C /-
 theorem monic_prod_multiset_X_sub_C : Monic (p.roots.map fun a => X - C a).Prod :=
   monic_multiset_prod_of_monic _ _ fun a _ => monic_X_sub_C a
 #align polynomial.monic_prod_multiset_X_sub_C Polynomial.monic_prod_multiset_X_sub_C
+-/
 
+#print Polynomial.prod_multiset_root_eq_finset_root /-
 theorem prod_multiset_root_eq_finset_root :
     (p.roots.map fun a => X - C a).Prod =
       p.roots.toFinset.Prod fun a => (X - C a) ^ rootMultiplicity a p :=
   by simp only [count_roots, Finset.prod_multiset_map_count]
 #align polynomial.prod_multiset_root_eq_finset_root Polynomial.prod_multiset_root_eq_finset_root
+-/
 
+#print Polynomial.prod_multiset_X_sub_C_dvd /-
 /-- The product `∏ (X - a)` for `a` inside the multiset `p.roots` divides `p`. -/
 theorem prod_multiset_X_sub_C_dvd (p : R[X]) : (p.roots.map fun a => X - C a).Prod ∣ p :=
   by
@@ -1124,7 +1301,9 @@ theorem prod_multiset_X_sub_C_dvd (p : R[X]) : (p.roots.map fun a => X - C a).Pr
     exact (pairwise_coprime_X_sub_C (IsFractionRing.injective R <| FractionRing R) h).pow
   · exact Polynomial.map_dvd _ (pow_root_multiplicity_dvd p a)
 #align polynomial.prod_multiset_X_sub_C_dvd Polynomial.prod_multiset_X_sub_C_dvd
+-/
 
+#print Multiset.prod_X_sub_C_dvd_iff_le_roots /-
 /-- A Galois connection. -/
 theorem Multiset.prod_X_sub_C_dvd_iff_le_roots {p : R[X]} (hp : p ≠ 0) (s : Multiset R) :
     (s.map fun a => X - C a).Prod ∣ p ↔ s ≤ p.roots :=
@@ -1137,7 +1316,9 @@ theorem Multiset.prod_X_sub_C_dvd_iff_le_roots {p : R[X]} (hp : p ≠ 0) (s : Mu
     fun h =>
     (Multiset.prod_dvd_prod_of_le <| Multiset.map_le_map h).trans p.prod_multiset_X_sub_C_dvd⟩
 #align multiset.prod_X_sub_C_dvd_iff_le_roots Multiset.prod_X_sub_C_dvd_iff_le_roots
+-/
 
+#print Polynomial.exists_prod_multiset_X_sub_C_mul /-
 theorem exists_prod_multiset_X_sub_C_mul (p : R[X]) :
     ∃ q,
       (p.roots.map fun a => X - C a).Prod * q = p ∧
@@ -1154,7 +1335,9 @@ theorem exists_prod_multiset_X_sub_C_mul (p : R[X]) :
     rw [roots_mul, roots_multiset_prod_X_sub_C] at he 
     exacts [add_right_eq_self.1 he, mul_ne_zero monic_prod_multiset_X_sub_C.ne_zero hq]
 #align polynomial.exists_prod_multiset_X_sub_C_mul Polynomial.exists_prod_multiset_X_sub_C_mul
+-/
 
+#print Polynomial.C_leadingCoeff_mul_prod_multiset_X_sub_C /-
 /-- A polynomial `p` that has as many roots as its degree
 can be written `p = p.leading_coeff * ∏(X - a)`, for `a` in `p.roots`. -/
 theorem C_leadingCoeff_mul_prod_multiset_X_sub_C (hroots : p.roots.card = p.natDegree) :
@@ -1163,13 +1346,16 @@ theorem C_leadingCoeff_mul_prod_multiset_X_sub_C (hroots : p.roots.card = p.natD
       p.prod_multiset_X_sub_C_dvd
       ((natDegree_multiset_prod_X_sub_C_eq_card _).trans hroots).ge).symm
 #align polynomial.C_leading_coeff_mul_prod_multiset_X_sub_C Polynomial.C_leadingCoeff_mul_prod_multiset_X_sub_C
+-/
 
+#print Polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq /-
 /-- A monic polynomial `p` that has as many roots as its degree
 can be written `p = ∏(X - a)`, for `a` in `p.roots`. -/
 theorem prod_multiset_X_sub_C_of_monic_of_roots_card_eq (hp : p.Monic)
     (hroots : p.roots.card = p.natDegree) : (p.roots.map fun a => X - C a).Prod = p := by
   convert C_leading_coeff_mul_prod_multiset_X_sub_C hroots; rw [hp.leading_coeff, C_1, one_mul]
 #align polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq Polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq
+-/
 
 end CommRing
 
@@ -1177,6 +1363,7 @@ section
 
 variable {A B : Type _} [CommRing A] [CommRing B]
 
+#print Polynomial.le_rootMultiplicity_map /-
 theorem le_rootMultiplicity_map {p : A[X]} {f : A →+* B} (hmap : map f p ≠ 0) (a : A) :
     rootMultiplicity a p ≤ rootMultiplicity (f a) (p.map f) :=
   by
@@ -1184,7 +1371,9 @@ theorem le_rootMultiplicity_map {p : A[X]} {f : A →+* B} (hmap : map f p ≠ 0
   refine' trans _ ((map_ring_hom f).map_dvd (pow_root_multiplicity_dvd p a))
   rw [map_pow, map_sub, coe_map_ring_hom, map_X, map_C]
 #align polynomial.le_root_multiplicity_map Polynomial.le_rootMultiplicity_map
+-/
 
+#print Polynomial.eq_rootMultiplicity_map /-
 theorem eq_rootMultiplicity_map {p : A[X]} {f : A →+* B} (hf : Function.Injective f) (a : A) :
     rootMultiplicity a p = rootMultiplicity (f a) (p.map f) :=
   by
@@ -1194,7 +1383,9 @@ theorem eq_rootMultiplicity_map {p : A[X]} {f : A →+* B} (hf : Function.Inject
     Polynomial.map_pow, Polynomial.map_sub, map_X, map_C]
   apply pow_root_multiplicity_dvd
 #align polynomial.eq_root_multiplicity_map Polynomial.eq_rootMultiplicity_map
+-/
 
+#print Polynomial.count_map_roots /-
 theorem count_map_roots [IsDomain A] {p : A[X]} {f : A →+* B} (hmap : map f p ≠ 0) (b : B) :
     (p.roots.map f).count b ≤ rootMultiplicity b (p.map f) :=
   by
@@ -1207,7 +1398,9 @@ theorem count_map_roots [IsDomain A] {p : A[X]} {f : A →+* B} (hmap : map f p
   congr; ext1
   simp only [Function.comp_apply, Polynomial.map_sub, map_X, map_C]
 #align polynomial.count_map_roots Polynomial.count_map_roots
+-/
 
+#print Polynomial.count_map_roots_of_injective /-
 theorem count_map_roots_of_injective [IsDomain A] (p : A[X]) {f : A →+* B}
     (hf : Function.Injective f) (b : B) : (p.roots.map f).count b ≤ rootMultiplicity b (p.map f) :=
   by
@@ -1217,31 +1410,41 @@ theorem count_map_roots_of_injective [IsDomain A] (p : A[X]) {f : A →+* B}
       root_multiplicity_zero]
   · exact count_map_roots ((Polynomial.map_ne_zero_iff hf).mpr hp0) b
 #align polynomial.count_map_roots_of_injective Polynomial.count_map_roots_of_injective
+-/
 
+#print Polynomial.map_roots_le /-
 theorem map_roots_le [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (h : p.map f ≠ 0) :
     p.roots.map f ≤ (p.map f).roots :=
   Multiset.le_iff_count.2 fun b => by rw [count_roots]; apply count_map_roots h
 #align polynomial.map_roots_le Polynomial.map_roots_le
+-/
 
+#print Polynomial.map_roots_le_of_injective /-
 theorem map_roots_le_of_injective [IsDomain A] [IsDomain B] (p : A[X]) {f : A →+* B}
     (hf : Function.Injective f) : p.roots.map f ≤ (p.map f).roots :=
   by
   by_cases hp0 : p = 0; · simp only [hp0, roots_zero, Multiset.map_zero, Polynomial.map_zero]
   exact map_roots_le ((Polynomial.map_ne_zero_iff hf).mpr hp0)
 #align polynomial.map_roots_le_of_injective Polynomial.map_roots_le_of_injective
+-/
 
+#print Polynomial.card_roots_le_map /-
 theorem card_roots_le_map [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (h : p.map f ≠ 0) :
     p.roots.card ≤ (p.map f).roots.card := by rw [← p.roots.card_map f];
   exact Multiset.card_le_of_le (map_roots_le h)
 #align polynomial.card_roots_le_map Polynomial.card_roots_le_map
+-/
 
+#print Polynomial.card_roots_le_map_of_injective /-
 theorem card_roots_le_map_of_injective [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B}
     (hf : Function.Injective f) : p.roots.card ≤ (p.map f).roots.card :=
   by
   by_cases hp0 : p = 0; · simp only [hp0, roots_zero, Polynomial.map_zero, Multiset.card_zero]
   exact card_roots_le_map ((Polynomial.map_ne_zero_iff hf).mpr hp0)
 #align polynomial.card_roots_le_map_of_injective Polynomial.card_roots_le_map_of_injective
+-/
 
+#print Polynomial.roots_map_of_injective_of_card_eq_natDegree /-
 theorem roots_map_of_injective_of_card_eq_natDegree [IsDomain A] [IsDomain B] {p : A[X]}
     {f : A →+* B} (hf : Function.Injective f) (hroots : p.roots.card = p.natDegree) :
     p.roots.map f = (p.map f).roots :=
@@ -1249,6 +1452,7 @@ theorem roots_map_of_injective_of_card_eq_natDegree [IsDomain A] [IsDomain B] {p
   apply Multiset.eq_of_le_of_card_le (map_roots_le_of_injective p hf)
   simpa only [Multiset.card_map, hroots] using (card_roots' _).trans (nat_degree_map_le f p)
 #align polynomial.roots_map_of_injective_of_card_eq_nat_degree Polynomial.roots_map_of_injective_of_card_eq_natDegree
+-/
 
 end
 
@@ -1256,6 +1460,7 @@ section
 
 variable [Semiring R] [CommRing S] [IsDomain S] (φ : R →+* S)
 
+#print Polynomial.isUnit_of_isUnit_leadingCoeff_of_isUnit_map /-
 theorem isUnit_of_isUnit_leadingCoeff_of_isUnit_map {f : R[X]} (hf : IsUnit f.leadingCoeff)
     (H : IsUnit (map φ f)) : IsUnit f :=
   by
@@ -1272,6 +1477,7 @@ theorem isUnit_of_isUnit_leadingCoeff_of_isUnit_map {f : R[X]} (hf : IsUnit f.le
     rw [h] at u 
     simpa using u
 #align polynomial.is_unit_of_is_unit_leading_coeff_of_is_unit_map Polynomial.isUnit_of_isUnit_leadingCoeff_of_isUnit_map
+-/
 
 end
 
@@ -1279,6 +1485,7 @@ section
 
 variable [CommRing R] [IsDomain R] [CommRing S] [IsDomain S] (φ : R →+* S)
 
+#print Polynomial.Monic.irreducible_of_irreducible_map /-
 /-- A polynomial over an integral domain `R` is irreducible if it is monic and
   irreducible after mapping into an integral domain `S`.
 
@@ -1298,6 +1505,7 @@ theorem Monic.irreducible_of_irreducible_map (f : R[X]) (h_mon : Monic f)
     apply isUnit_of_mul_eq_one
   · exact q; · rw [mul_comm]; exact q
 #align polynomial.monic.irreducible_of_irreducible_map Polynomial.Monic.irreducible_of_irreducible_map
+-/
 
 end
 

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

@@ -514,8 +514,7 @@ theorem exists_multiset_roots :
           (card (x ::ₘ t) : WithBot ℕ) = t.card + 1 := by exact_mod_cast card_cons _ _
           _ ≤ degree p := by
             rw [← degree_add_div_by_monic (monic_X_sub_C x) hdeg, degree_X_sub_C, add_comm] <;>
-              exact add_le_add (le_refl (1 : WithBot ℕ)) htd
-          ,
+              exact add_le_add (le_refl (1 : WithBot ℕ)) htd,
         by
         intro a
         conv_rhs => rw [← mul_div_by_monic_eq_iff_is_root.mpr hx]
@@ -564,7 +563,6 @@ theorem card_roots_sub_C {p : R[X]} {a : R} (hp0 : 0 < degree p) :
     ((p - C a).roots.card : WithBot ℕ) ≤ degree (p - C a) :=
       card_roots <| mt sub_eq_zero.1 fun h => not_le_of_gt hp0 <| h.symm ▸ degree_C_le
     _ = degree p := by rw [sub_eq_add_neg, ← C_neg] <;> exact degree_add_C hp0
-    
 #align polynomial.card_roots_sub_C Polynomial.card_roots_sub_C
 
 theorem card_roots_sub_C' {p : R[X]} {a : R} (hp0 : 0 < degree p) :
@@ -789,7 +787,6 @@ theorem card_roots_X_pow_sub_C {n : ℕ} (hn : 0 < n) (a : R) :
       ((roots ((X : R[X]) ^ n - C a)).card : WithBot ℕ) ≤ degree ((X : R[X]) ^ n - C a) :=
         card_roots (X_pow_sub_C_ne_zero hn a)
       _ = n := degree_X_pow_sub_C hn a
-      
 #align polynomial.card_roots_X_pow_sub_C Polynomial.card_roots_X_pow_sub_C
 
 section NthRoots

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

@@ -618,13 +618,13 @@ theorem card_le_degree_of_subset_roots {p : R[X]} {Z : Finset R} (h : Z.val ⊆
 -/
 
 #print Polynomial.finite_setOf_isRoot /-
-theorem finite_setOf_isRoot {p : R[X]} (hp : p ≠ 0) : Set.Finite { x | IsRoot p x } := by
+theorem finite_setOf_isRoot {p : R[X]} (hp : p ≠ 0) : Set.Finite {x | IsRoot p x} := by
   simpa only [← Finset.setOf_mem, mem_to_finset, mem_roots hp] using p.roots.to_finset.finite_to_set
 #align polynomial.finite_set_of_is_root Polynomial.finite_setOf_isRoot
 -/
 
 #print Polynomial.eq_zero_of_infinite_isRoot /-
-theorem eq_zero_of_infinite_isRoot (p : R[X]) (h : Set.Infinite { x | IsRoot p x }) : p = 0 :=
+theorem eq_zero_of_infinite_isRoot (p : R[X]) (h : Set.Infinite {x | IsRoot p x}) : p = 0 :=
   not_imp_comm.mp finite_setOf_isRoot h
 #align polynomial.eq_zero_of_infinite_is_root Polynomial.eq_zero_of_infinite_isRoot
 -/
@@ -642,8 +642,8 @@ theorem exists_min_root [LinearOrder R] (p : R[X]) (hp : p ≠ 0) : ∃ x₀, 
 -/
 
 #print Polynomial.eq_of_infinite_eval_eq /-
-theorem eq_of_infinite_eval_eq (p q : R[X]) (h : Set.Infinite { x | eval x p = eval x q }) :
-    p = q := by
+theorem eq_of_infinite_eval_eq (p q : R[X]) (h : Set.Infinite {x | eval x p = eval x q}) : p = q :=
+  by
   rw [← sub_eq_zero]
   apply eq_zero_of_infinite_is_root
   simpa only [is_root, eval_sub, sub_eq_zero]
@@ -900,9 +900,9 @@ theorem comp_eq_zero_iff : p.comp q = 0 ↔ p = 0 ∨ p.eval (q.coeff 0) = 0 ∧
 
 theorem zero_of_eval_zero [Infinite R] (p : R[X]) (h : ∀ x, p.eval x = 0) : p = 0 := by
   classical by_contra hp <;>
-      exact
-        Fintype.false
-          ⟨p.roots.to_finset, fun x => multiset.mem_to_finset.mpr ((mem_roots hp).mpr (h _))⟩
+    exact
+      Fintype.false
+        ⟨p.roots.to_finset, fun x => multiset.mem_to_finset.mpr ((mem_roots hp).mpr (h _))⟩
 #align polynomial.zero_of_eval_zero Polynomial.zero_of_eval_zero
 
 #print Polynomial.funext /-

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

@@ -182,13 +182,13 @@ theorem degree_le_mul_left (p : R[X]) (hq : q ≠ 0) : degree p ≤ degree (p *
 
 theorem natDegree_le_of_dvd {p q : R[X]} (h1 : p ∣ q) (h2 : q ≠ 0) : p.natDegree ≤ q.natDegree :=
   by
-  rcases h1 with ⟨q, rfl⟩; rw [mul_ne_zero_iff] at h2
+  rcases h1 with ⟨q, rfl⟩; rw [mul_ne_zero_iff] at h2 
   rw [nat_degree_mul h2.1 h2.2]; exact Nat.le_add_right _ _
 #align polynomial.nat_degree_le_of_dvd Polynomial.natDegree_le_of_dvd
 
 theorem degree_le_of_dvd {p q : R[X]} (h1 : p ∣ q) (h2 : q ≠ 0) : degree p ≤ degree q :=
   by
-  rcases h1 with ⟨q, rfl⟩; rw [mul_ne_zero_iff] at h2
+  rcases h1 with ⟨q, rfl⟩; rw [mul_ne_zero_iff] at h2 
   exact degree_le_mul_left p h2.2
 #align polynomial.degree_le_of_dvd Polynomial.degree_le_of_dvd
 
@@ -231,7 +231,7 @@ theorem natDegree_eq_zero_of_isUnit (h : IsUnit p) : natDegree p = 0 :=
   nontriviality R
   obtain ⟨q, hq⟩ := h.exists_right_inv
   have := nat_degree_mul (left_ne_zero_of_mul_eq_one hq) (right_ne_zero_of_mul_eq_one hq)
-  rw [hq, nat_degree_one, eq_comm, add_eq_zero_iff] at this
+  rw [hq, nat_degree_one, eq_comm, add_eq_zero_iff] at this 
   exact this.1
 #align polynomial.nat_degree_eq_zero_of_is_unit Polynomial.natDegree_eq_zero_of_isUnit
 
@@ -327,7 +327,7 @@ theorem Monic.irreducible_iff_natDegree' (hp : p.Monic) :
   constructor <;> intro h f g hf hg he <;> subst he
   · rw [hf.nat_degree_mul hg, add_le_add_iff_right]
     exact fun ha => (h f g hf hg rfl).elim (ha.1.trans_le ha.2).ne' ha.1.ne'
-  · simp_rw [hf.nat_degree_mul hg, pos_iff_ne_zero] at h
+  · simp_rw [hf.nat_degree_mul hg, pos_iff_ne_zero] at h 
     contrapose! h
     obtain hl | hl := le_total f.nat_degree g.nat_degree
     · exact ⟨g, f, hg, hf, mul_comm g f, h.1, add_le_add_left hl _⟩
@@ -342,7 +342,7 @@ theorem Monic.not_irreducible_iff_exists_add_mul_eq_coeff (hm : p.Monic) (hnd :
   rw [hm.irreducible_iff_nat_degree', and_iff_right, hnd]
   push_neg; constructor
   · rintro ⟨a, b, ha, hb, rfl, hdb | ⟨⟨⟩⟩⟩
-    have hda := hnd; rw [ha.nat_degree_mul hb, hdb] at hda
+    have hda := hnd; rw [ha.nat_degree_mul hb, hdb] at hda 
     use a.coeff 0, b.coeff 0, mul_coeff_zero a b
     simpa only [next_coeff, hnd, add_right_cancel hda, hdb] using ha.next_coeff_mul hb
   · rintro ⟨c₁, c₂, hmul, hadd⟩
@@ -444,10 +444,10 @@ theorem Monic.irreducible_of_degree_eq_one (hp1 : degree p = 1) (hm : Monic p) :
 theorem eq_of_monic_of_associated (hp : p.Monic) (hq : q.Monic) (hpq : Associated p q) : p = q :=
   by
   obtain ⟨u, hu⟩ := hpq
-  unfold monic at hp hq
-  rw [eq_C_of_degree_le_zero (degree_coe_units _).le] at hu
-  rw [← hu, leading_coeff_mul, hp, one_mul, leading_coeff_C] at hq
-  rwa [hq, C_1, mul_one] at hu
+  unfold monic at hp hq 
+  rw [eq_C_of_degree_le_zero (degree_coe_units _).le] at hu 
+  rw [← hu, leading_coeff_mul, hp, one_mul, leading_coeff_C] at hq 
+  rwa [hq, C_1, mul_one] at hu 
   all_goals infer_instance
 #align polynomial.eq_of_monic_of_associated Polynomial.eq_of_monic_of_associated
 
@@ -484,7 +484,7 @@ theorem rootMultiplicity_X_sub_C_pow (a : R) (n : ℕ) : rootMultiplicity a ((X
   · refine' root_multiplicity_eq_zero _
     simp only [eval_one, is_root.def, not_false_iff, one_ne_zero, pow_zero]
   have hzero := pow_ne_zero n.succ (X_sub_C_ne_zero a)
-  rw [pow_succ (X - C a) n] at hzero⊢
+  rw [pow_succ (X - C a) n] at hzero ⊢
   simp only [root_multiplicity_mul hzero, root_multiplicity_X_sub_C_self, hn, Nat.one_add]
 #align polynomial.root_multiplicity_X_sub_C_pow Polynomial.rootMultiplicity_X_sub_C_pow
 
@@ -497,14 +497,15 @@ theorem exists_multiset_roots :
       let ⟨x, hx⟩ := h
       have hpd : 0 < degree p := degree_pos_of_root hp hx
       have hd0 : p /ₘ (X - C x) ≠ 0 := fun h => by
-        rw [← mul_div_by_monic_eq_iff_is_root.2 hx, h, MulZeroClass.mul_zero] at hp <;> exact hp rfl
+        rw [← mul_div_by_monic_eq_iff_is_root.2 hx, h, MulZeroClass.mul_zero] at hp  <;>
+          exact hp rfl
       have wf : degree (p /ₘ _) < degree p :=
         degree_div_by_monic_lt _ (monic_X_sub_C x) hp ((degree_X_sub_C x).symm ▸ by decide)
       let ⟨t, htd, htr⟩ := @exists_multiset_roots (p /ₘ (X - C x)) hd0
       have hdeg : degree (X - C x) ≤ degree p :=
         by
         rw [degree_X_sub_C, degree_eq_nat_degree hp]
-        rw [degree_eq_nat_degree hp] at hpd
+        rw [degree_eq_nat_degree hp] at hpd 
         exact WithBot.coe_le_coe.2 (WithBot.coe_lt_coe.1 hpd)
       have hdiv0 : p /ₘ (X - C x) ≠ 0 :=
         mt (div_by_monic_eq_zero_iff (monic_X_sub_C x)).1 <| not_lt.2 hdeg
@@ -714,7 +715,7 @@ theorem roots_list_prod (L : List R[X]) :
     (0 : R[X]) ∉ L → L.Prod.roots = (L : Multiset R[X]).bind roots :=
   List.recOn L (fun _ => roots_one) fun hd tl ih H =>
     by
-    rw [List.mem_cons, not_or] at H
+    rw [List.mem_cons, not_or] at H 
     rw [List.prod_cons, roots_mul (mul_ne_zero (Ne.symm H.1) <| List.prod_ne_zero H.2), ←
       Multiset.cons_coe, Multiset.cons_bind, ih H.2]
 #align polynomial.roots_list_prod Polynomial.roots_list_prod
@@ -863,7 +864,7 @@ theorem Monic.comp (hp : p.Monic) (hq : q.Monic) (h : q.natDegree ≠ 0) : (p.co
 theorem Monic.comp_X_add_C (hp : p.Monic) (r : R) : (p.comp (X + C r)).Monic :=
   by
   refine' hp.comp (monic_X_add_C _) fun ha => _
-  rw [nat_degree_X_add_C] at ha
+  rw [nat_degree_X_add_C] at ha 
   exact one_ne_zero ha
 #align polynomial.monic.comp_X_add_C Polynomial.Monic.comp_X_add_C
 
@@ -888,9 +889,9 @@ theorem comp_eq_zero_iff : p.comp q = 0 ↔ p = 0 ∨ p.eval (q.coeff 0) = 0 ∧
       rw [← mul_eq_zero, ← nat_degree_comp, h, nat_degree_zero]
     replace key := Or.imp eq_C_of_nat_degree_eq_zero eq_C_of_nat_degree_eq_zero key
     cases key
-    · rw [key, C_comp] at h
+    · rw [key, C_comp] at h 
       exact Or.inl (key.trans h)
-    · rw [key, comp_C, C_eq_zero] at h
+    · rw [key, comp_C, C_eq_zero] at h 
       exact Or.inr ⟨h, key⟩
   ·
     exact fun h =>
@@ -992,14 +993,14 @@ theorem rootSet_maps_to' {p : T[X]} {S S'} [CommRing S] [IsDomain S] [Algebra T
     [IsDomain S'] [Algebra T S'] (hp : p.map (algebraMap T S') = 0 → p.map (algebraMap T S) = 0)
     (f : S →ₐ[T] S') : (p.rootSet S).MapsTo f (p.rootSet S') := fun x hx =>
   by
-  rw [mem_root_set'] at hx⊢
+  rw [mem_root_set'] at hx ⊢
   rw [aeval_alg_hom, AlgHom.comp_apply, hx.2, _root_.map_zero]
   exact ⟨mt hp hx.1, rfl⟩
 #align polynomial.root_set_maps_to' Polynomial.rootSet_maps_to'
 
 #print Polynomial.ne_zero_of_mem_rootSet /-
 theorem ne_zero_of_mem_rootSet {p : T[X]} [CommRing S] [IsDomain S] [Algebra T S] {a : S}
-    (h : a ∈ p.rootSet S) : p ≠ 0 := fun hf => by rwa [hf, root_set_zero] at h
+    (h : a ∈ p.rootSet S) : p ≠ 0 := fun hf => by rwa [hf, root_set_zero] at h 
 #align polynomial.ne_zero_of_mem_root_set Polynomial.ne_zero_of_mem_rootSet
 -/
 
@@ -1041,7 +1042,7 @@ theorem degree_eq_one_of_irreducible_of_root (hi : Irreducible p) {x : R} (hx :
     (fun h => by
       have h₁ : degree (X - C x) = 1 := degree_X_sub_C x
       have h₂ : degree (X - C x) = 0 := degree_eq_zero_of_isUnit h
-      rw [h₁] at h₂ <;> exact absurd h₂ (by decide))
+      rw [h₁] at h₂  <;> exact absurd h₂ (by decide))
     fun hgu => by rw [hg, degree_mul, degree_X_sub_C, degree_eq_zero_of_is_unit hgu, add_zero]
 #align polynomial.degree_eq_one_of_irreducible_of_root Polynomial.degree_eq_one_of_irreducible_of_root
 
@@ -1077,9 +1078,9 @@ theorem eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le {R} [CommRing R] {p
   obtain ⟨r, hr⟩ := hdiv
   obtain rfl | hq := eq_or_ne q 0; · simp
   have rzero : r ≠ 0 := fun h => by simpa [h, hq] using hr
-  rw [hr, nat_degree_mul'] at hdeg; swap
+  rw [hr, nat_degree_mul'] at hdeg ; swap
   · rw [hp.leading_coeff, one_mul, leading_coeff_ne_zero]; exact rzero
-  rw [mul_comm, @eq_C_of_nat_degree_eq_zero _ _ r] at hr
+  rw [mul_comm, @eq_C_of_nat_degree_eq_zero _ _ r] at hr 
   · convert hr; convert leading_coeff_C _ using 1; rw [hr, leading_coeff_mul_monic hp]
   · exact (add_right_inj _).1 (le_antisymm hdeg <| Nat.le.intro rfl)
 #align polynomial.eq_leading_coeff_mul_of_monic_of_dvd_of_nat_degree_le Polynomial.eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le
@@ -1148,13 +1149,13 @@ theorem exists_prod_multiset_X_sub_C_mul (p : R[X]) :
   obtain ⟨q, he⟩ := p.prod_multiset_X_sub_C_dvd
   use q, he.symm
   obtain rfl | hq := eq_or_ne q 0
-  · rw [MulZeroClass.mul_zero] at he; subst he; simp
+  · rw [MulZeroClass.mul_zero] at he ; subst he; simp
   constructor
   · conv_rhs => rw [he]
     rw [monic_prod_multiset_X_sub_C.nat_degree_mul' hq, nat_degree_multiset_prod_X_sub_C_eq_card]
   · replace he := congr_arg roots he.symm
-    rw [roots_mul, roots_multiset_prod_X_sub_C] at he
-    exacts[add_right_eq_self.1 he, mul_ne_zero monic_prod_multiset_X_sub_C.ne_zero hq]
+    rw [roots_mul, roots_multiset_prod_X_sub_C] at he 
+    exacts [add_right_eq_self.1 he, mul_ne_zero monic_prod_multiset_X_sub_C.ne_zero hq]
 #align polynomial.exists_prod_multiset_X_sub_C_mul Polynomial.exists_prod_multiset_X_sub_C_mul
 
 /-- A polynomial `p` that has as many roots as its degree
@@ -1206,7 +1207,7 @@ theorem count_map_roots [IsDomain A] {p : A[X]} {f : A →+* B} (hmap : map f p
   refine' (Multiset.prod_dvd_prod_of_le <| Multiset.map_le_map <| Multiset.filter_le _ _).trans _
   convert Polynomial.map_dvd _ p.prod_multiset_X_sub_C_dvd
   simp only [Polynomial.map_multiset_prod, Multiset.map_map]
-  congr ; ext1
+  congr; ext1
   simp only [Function.comp_apply, Polynomial.map_sub, map_X, map_C]
 #align polynomial.count_map_roots Polynomial.count_map_roots
 
@@ -1262,7 +1263,7 @@ theorem isUnit_of_isUnit_leadingCoeff_of_isUnit_map {f : R[X]} (hf : IsUnit f.le
     (H : IsUnit (map φ f)) : IsUnit f :=
   by
   have dz := degree_eq_zero_of_is_unit H
-  rw [degree_map_eq_of_leading_coeff_ne_zero] at dz
+  rw [degree_map_eq_of_leading_coeff_ne_zero] at dz 
   · rw [eq_C_of_degree_eq_zero dz]
     refine' IsUnit.map C _
     convert hf
@@ -1271,7 +1272,7 @@ theorem isUnit_of_isUnit_leadingCoeff_of_isUnit_map {f : R[X]} (hf : IsUnit f.le
     simpa using H
   · intro h
     have u : IsUnit (φ f.leading_coeff) := IsUnit.map φ hf
-    rw [h] at u
+    rw [h] at u 
     simpa using u
 #align polynomial.is_unit_of_is_unit_leading_coeff_of_is_unit_map Polynomial.isUnit_of_isUnit_leadingCoeff_of_isUnit_map
 
@@ -1291,9 +1292,9 @@ theorem Monic.irreducible_of_irreducible_map (f : R[X]) (h_mon : Monic f)
     (h_irr : Irreducible (map φ f)) : Irreducible f :=
   by
   refine' ⟨h_irr.not_unit ∘ IsUnit.map (map_ring_hom φ), fun a b h => _⟩
-  dsimp [monic] at h_mon
+  dsimp [monic] at h_mon 
   have q := (leading_coeff_mul a b).symm
-  rw [← h, h_mon] at q
+  rw [← h, h_mon] at q 
   refine'
         (h_irr.is_unit_or_is_unit <| (congr_arg (map φ) h).trans (Polynomial.map_mul φ)).imp _ _ <;>
       apply is_unit_of_is_unit_leading_coeff_of_is_unit_map <;>

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

@@ -58,19 +58,15 @@ section
 
 variable [Semiring S]
 
-#print Polynomial.natDegree_pos_of_aeval_root /-
 theorem natDegree_pos_of_aeval_root [Algebra R S] {p : R[X]} (hp : p ≠ 0) {z : S}
     (hz : aeval z p = 0) (inj : ∀ x : R, algebraMap R S x = 0 → x = 0) : 0 < p.natDegree :=
   natDegree_pos_of_eval₂_root hp (algebraMap R S) hz inj
 #align polynomial.nat_degree_pos_of_aeval_root Polynomial.natDegree_pos_of_aeval_root
--/
 
-#print Polynomial.degree_pos_of_aeval_root /-
 theorem degree_pos_of_aeval_root [Algebra R S] {p : R[X]} (hp : p ≠ 0) {z : S} (hz : aeval z p = 0)
     (inj : ∀ x : R, algebraMap R S x = 0 → x = 0) : 0 < p.degree :=
   natDegree_pos_iff_degree_pos.mp (natDegree_pos_of_aeval_root hp hz inj)
 #align polynomial.degree_pos_of_aeval_root Polynomial.degree_pos_of_aeval_root
--/
 
 #print Polynomial.modByMonic_eq_of_dvd_sub /-
 theorem modByMonic_eq_of_dvd_sub (hq : q.Monic) {p₁ p₂ : R[X]} (h : q ∣ p₁ - p₂) :
@@ -128,14 +124,12 @@ section
 
 variable [Ring S]
 
-#print Polynomial.aeval_modByMonic_eq_self_of_root /-
 theorem aeval_modByMonic_eq_self_of_root [Algebra R S] {p q : R[X]} (hq : q.Monic) {x : S}
     (hx : aeval x q = 0) : aeval x (p %ₘ q) = aeval x p :=
   by-- `eval₂_mod_by_monic_eq_self_of_root` doesn't work here as it needs commutativity
   rw [mod_by_monic_eq_sub_mul_div p hq, _root_.map_sub, _root_.map_mul, hx, MulZeroClass.zero_mul,
     sub_zero]
 #align polynomial.aeval_mod_by_monic_eq_self_of_root Polynomial.aeval_modByMonic_eq_self_of_root
--/
 
 end
 
@@ -1009,12 +1003,10 @@ theorem ne_zero_of_mem_rootSet {p : T[X]} [CommRing S] [IsDomain S] [Algebra T S
 #align polynomial.ne_zero_of_mem_root_set Polynomial.ne_zero_of_mem_rootSet
 -/
 
-#print Polynomial.aeval_eq_zero_of_mem_rootSet /-
 theorem aeval_eq_zero_of_mem_rootSet {p : T[X]} [CommRing S] [IsDomain S] [Algebra T S] {a : S}
     (hx : a ∈ p.rootSet S) : aeval a p = 0 :=
   (mem_rootSet'.1 hx).2
 #align polynomial.aeval_eq_zero_of_mem_root_set Polynomial.aeval_eq_zero_of_mem_rootSet
--/
 
 theorem rootSet_mapsTo {p : T[X]} {S S'} [CommRing S] [IsDomain S] [Algebra T S] [CommRing S']
     [IsDomain S'] [Algebra T S'] [NoZeroSMulDivisors T S'] (f : S →ₐ[T] S') :

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

@@ -40,7 +40,7 @@ This file starts looking like the ring theory of $ R[X] $
 
 noncomputable section
 
-open Classical Polynomial
+open scoped Classical Polynomial
 
 open Finset
 
@@ -634,13 +634,17 @@ theorem eq_zero_of_infinite_isRoot (p : R[X]) (h : Set.Infinite { x | IsRoot p x
 #align polynomial.eq_zero_of_infinite_is_root Polynomial.eq_zero_of_infinite_isRoot
 -/
 
+#print Polynomial.exists_max_root /-
 theorem exists_max_root [LinearOrder R] (p : R[X]) (hp : p ≠ 0) : ∃ x₀, ∀ x, p.IsRoot x → x ≤ x₀ :=
   Set.exists_upper_bound_image _ _ <| finite_setOf_isRoot hp
 #align polynomial.exists_max_root Polynomial.exists_max_root
+-/
 
+#print Polynomial.exists_min_root /-
 theorem exists_min_root [LinearOrder R] (p : R[X]) (hp : p ≠ 0) : ∃ x₀, ∀ x, p.IsRoot x → x₀ ≤ x :=
   Set.exists_lower_bound_image _ _ <| finite_setOf_isRoot hp
 #align polynomial.exists_min_root Polynomial.exists_min_root
+-/
 
 #print Polynomial.eq_of_infinite_eval_eq /-
 theorem eq_of_infinite_eval_eq (p q : R[X]) (h : Set.Infinite { x | eval x p = eval x q }) :
@@ -1049,6 +1053,7 @@ theorem degree_eq_one_of_irreducible_of_root (hi : Irreducible p) {x : R} (hx :
     fun hgu => by rw [hg, degree_mul, degree_X_sub_C, degree_eq_zero_of_is_unit hgu, add_zero]
 #align polynomial.degree_eq_one_of_irreducible_of_root Polynomial.degree_eq_one_of_irreducible_of_root
 
+#print Polynomial.leadingCoeff_divByMonic_of_monic /-
 /-- Division by a monic polynomial doesn't change the leading coefficient. -/
 theorem leadingCoeff_divByMonic_of_monic {R : Type u} [CommRing R] {p q : R[X]} (hmonic : q.Monic)
     (hdegree : q.degree ≤ p.degree) : (p /ₘ q).leadingCoeff = p.leadingCoeff :=
@@ -1062,6 +1067,7 @@ theorem leadingCoeff_divByMonic_of_monic {R : Type u} [CommRing R] {p q : R[X]}
   rw [degree_mul' h, degree_add_div_by_monic hmonic hdegree]
   exact (degree_mod_by_monic_lt p hmonic).trans_le hdegree
 #align polynomial.leading_coeff_div_by_monic_of_monic Polynomial.leadingCoeff_divByMonic_of_monic
+-/
 
 theorem leadingCoeff_divByMonic_X_sub_C (p : R[X]) (hp : degree p ≠ 0) (a : R) :
     leadingCoeff (p /ₘ (X - C a)) = leadingCoeff p :=

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

@@ -152,24 +152,12 @@ instance : NoZeroDivisors R[X]
     refine' eq_zero_or_eq_zero_of_mul_eq_zero _
     rw [← leading_coeff_zero, ← leading_coeff_mul, h]
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_mul Polynomial.natDegree_mulₓ'. -/
 theorem natDegree_mul (hp : p ≠ 0) (hq : q ≠ 0) : natDegree (p * q) = natDegree p + natDegree q :=
   by
   rw [← WithBot.coe_eq_coe, ← degree_eq_nat_degree (mul_ne_zero hp hq), WithBot.coe_add, ←
     degree_eq_nat_degree hp, ← degree_eq_nat_degree hq, degree_mul]
 #align polynomial.nat_degree_mul Polynomial.natDegree_mul
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.trailing_degree_mul Polynomial.trailingDegree_mulₓ'. -/
 theorem trailingDegree_mul : (p * q).trailingDegree = p.trailingDegree + q.trailingDegree :=
   by
   by_cases hp : p = 0
@@ -181,12 +169,6 @@ theorem trailingDegree_mul : (p * q).trailingDegree = p.trailingDegree + q.trail
     WithTop.coe_add]
 #align polynomial.trailing_degree_mul Polynomial.trailingDegree_mul
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_pow Polynomial.natDegree_powₓ'. -/
 @[simp]
 theorem natDegree_pow (p : R[X]) (n : ℕ) : natDegree (p ^ n) = n * natDegree p :=
   if hp0 : p = 0 then
@@ -197,12 +179,6 @@ theorem natDegree_pow (p : R[X]) (n : ℕ) : natDegree (p ^ n) = n * natDegree p
       (by rw [← leading_coeff_pow, Ne.def, leading_coeff_eq_zero] <;> exact pow_ne_zero _ hp0)
 #align polynomial.nat_degree_pow Polynomial.natDegree_pow
 
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 theorem degree_le_mul_left (p : R[X]) (hq : q ≠ 0) : degree p ≤ degree (p * q) :=
   if hp : p = 0 then by simp only [hp, MulZeroClass.zero_mul, le_refl]
   else by
@@ -210,84 +186,42 @@ theorem degree_le_mul_left (p : R[X]) (hq : q ≠ 0) : degree p ≤ degree (p *
       exact WithBot.coe_le_coe.2 (Nat.le_add_right _ _)
 #align polynomial.degree_le_mul_left Polynomial.degree_le_mul_left
 
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 theorem natDegree_le_of_dvd {p q : R[X]} (h1 : p ∣ q) (h2 : q ≠ 0) : p.natDegree ≤ q.natDegree :=
   by
   rcases h1 with ⟨q, rfl⟩; rw [mul_ne_zero_iff] at h2
   rw [nat_degree_mul h2.1 h2.2]; exact Nat.le_add_right _ _
 #align polynomial.nat_degree_le_of_dvd Polynomial.natDegree_le_of_dvd
 
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 theorem degree_le_of_dvd {p q : R[X]} (h1 : p ∣ q) (h2 : q ≠ 0) : degree p ≤ degree q :=
   by
   rcases h1 with ⟨q, rfl⟩; rw [mul_ne_zero_iff] at h2
   exact degree_le_mul_left p h2.2
 #align polynomial.degree_le_of_dvd Polynomial.degree_le_of_dvd
 
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 theorem eq_zero_of_dvd_of_degree_lt {p q : R[X]} (h₁ : p ∣ q) (h₂ : degree q < degree p) : q = 0 :=
   by
   by_contra hc
   exact (lt_iff_not_ge _ _).mp h₂ (degree_le_of_dvd h₁ hc)
 #align polynomial.eq_zero_of_dvd_of_degree_lt Polynomial.eq_zero_of_dvd_of_degree_lt
 
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 theorem eq_zero_of_dvd_of_natDegree_lt {p q : R[X]} (h₁ : p ∣ q) (h₂ : natDegree q < natDegree p) :
     q = 0 := by
   by_contra hc
   exact (lt_iff_not_ge _ _).mp h₂ (nat_degree_le_of_dvd h₁ hc)
 #align polynomial.eq_zero_of_dvd_of_nat_degree_lt Polynomial.eq_zero_of_dvd_of_natDegree_lt
 
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 theorem not_dvd_of_degree_lt {p q : R[X]} (h0 : q ≠ 0) (hl : q.degree < p.degree) : ¬p ∣ q :=
   by
   by_contra hcontra
   exact h0 (eq_zero_of_dvd_of_degree_lt hcontra hl)
 #align polynomial.not_dvd_of_degree_lt Polynomial.not_dvd_of_degree_lt
 
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 theorem not_dvd_of_natDegree_lt {p q : R[X]} (h0 : q ≠ 0) (hl : q.natDegree < p.natDegree) :
     ¬p ∣ q := by
   by_contra hcontra
   exact h0 (eq_zero_of_dvd_of_nat_degree_lt hcontra hl)
 #align polynomial.not_dvd_of_nat_degree_lt Polynomial.not_dvd_of_natDegree_lt
 
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 /-- This lemma is useful for working with the `int_degree` of a rational function. -/
 theorem natDegree_sub_eq_of_prod_eq {p₁ p₂ q₁ q₂ : R[X]} (hp₁ : p₁ ≠ 0) (hq₁ : q₁ ≠ 0)
     (hp₂ : p₂ ≠ 0) (hq₂ : q₂ ≠ 0) (h_eq : p₁ * q₂ = p₂ * q₁) :
@@ -298,12 +232,6 @@ theorem natDegree_sub_eq_of_prod_eq {p₁ p₂ q₁ q₂ : R[X]} (hp₁ : p₁ 
   rw [← nat_degree_mul hp₁ hq₂, ← nat_degree_mul hp₂ hq₁, h_eq]
 #align polynomial.nat_degree_sub_eq_of_prod_eq Polynomial.natDegree_sub_eq_of_prod_eq
 
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 theorem natDegree_eq_zero_of_isUnit (h : IsUnit p) : natDegree p = 0 :=
   by
   nontriviality R
@@ -313,34 +241,16 @@ theorem natDegree_eq_zero_of_isUnit (h : IsUnit p) : natDegree p = 0 :=
   exact this.1
 #align polynomial.nat_degree_eq_zero_of_is_unit Polynomial.natDegree_eq_zero_of_isUnit
 
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 theorem degree_eq_zero_of_isUnit [Nontrivial R] (h : IsUnit p) : degree p = 0 :=
   (natDegree_eq_zero_iff_degree_le_zero.mp <| natDegree_eq_zero_of_isUnit h).antisymm
     (zero_le_degree_iff.mpr h.NeZero)
 #align polynomial.degree_eq_zero_of_is_unit Polynomial.degree_eq_zero_of_isUnit
 
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 @[simp]
 theorem degree_coe_units [Nontrivial R] (u : R[X]ˣ) : degree (u : R[X]) = 0 :=
   degree_eq_zero_of_isUnit ⟨u, rfl⟩
 #align polynomial.degree_coe_units Polynomial.degree_coe_units
 
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 theorem isUnit_iff : IsUnit p ↔ ∃ r : R, IsUnit r ∧ C r = p :=
   ⟨fun hp =>
     ⟨p.coeff 0,
@@ -389,12 +299,6 @@ section NoZeroDivisors
 
 variable [CommSemiring R] [NoZeroDivisors R] {p q : R[X]}
 
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 theorem irreducible_of_monic (hp : p.Monic) (hp1 : p ≠ 1) :
     Irreducible p ↔ ∀ f g : R[X], f.Monic → g.Monic → f * g = p → f = 1 ∨ g = 1 :=
   by
@@ -410,12 +314,6 @@ theorem irreducible_of_monic (hp : p.Monic) (hp1 : p ≠ 1) :
       mul_comm, ← hfg]
 #align polynomial.irreducible_of_monic Polynomial.irreducible_of_monic
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.monic.irreducible_iff_nat_degree Polynomial.Monic.irreducible_iff_natDegreeₓ'. -/
 theorem Monic.irreducible_iff_natDegree (hp : p.Monic) :
     Irreducible p ↔
       p ≠ 1 ∧ ∀ f g : R[X], f.Monic → g.Monic → f * g = p → f.natDegree = 0 ∨ g.natDegree = 0 :=
@@ -426,12 +324,6 @@ theorem Monic.irreducible_iff_natDegree (hp : p.Monic) :
   rw [ha.nat_degree_eq_zero_iff_eq_one, hb.nat_degree_eq_zero_iff_eq_one]
 #align polynomial.monic.irreducible_iff_nat_degree Polynomial.Monic.irreducible_iff_natDegree
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.monic.irreducible_iff_nat_degree' Polynomial.Monic.irreducible_iff_natDegree'ₓ'. -/
 theorem Monic.irreducible_iff_natDegree' (hp : p.Monic) :
     Irreducible p ↔
       p ≠ 1 ∧ ∀ f g : R[X], f.Monic → g.Monic → f * g = p → g.natDegree ∉ Ioc 0 (p.natDegree / 2) :=
@@ -448,12 +340,6 @@ theorem Monic.irreducible_iff_natDegree' (hp : p.Monic) :
     · exact ⟨f, g, hf, hg, rfl, h.2, add_le_add_right hl _⟩
 #align polynomial.monic.irreducible_iff_nat_degree' Polynomial.Monic.irreducible_iff_natDegree'
 
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 theorem Monic.not_irreducible_iff_exists_add_mul_eq_coeff (hm : p.Monic) (hnd : p.natDegree = 2) :
     ¬Irreducible p ↔ ∃ c₁ c₂, p.coeff 0 = c₁ * c₂ ∧ p.coeff 1 = c₁ + c₂ :=
   by
@@ -474,22 +360,10 @@ theorem Monic.not_irreducible_iff_exists_add_mul_eq_coeff (hm : p.Monic) (hnd :
   · rintro rfl; simpa only [nat_degree_one] using hnd
 #align polynomial.monic.not_irreducible_iff_exists_add_mul_eq_coeff Polynomial.Monic.not_irreducible_iff_exists_add_mul_eq_coeff
 
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 theorem root_mul : IsRoot (p * q) a ↔ IsRoot p a ∨ IsRoot q a := by
   simp_rw [is_root, eval_mul, mul_eq_zero]
 #align polynomial.root_mul Polynomial.root_mul
 
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 theorem root_or_root_of_root_mul (h : IsRoot (p * q) a) : IsRoot p a ∨ IsRoot q a :=
   root_mul.1 h
 #align polynomial.root_or_root_of_root_mul Polynomial.root_or_root_of_root_mul
@@ -509,9 +383,6 @@ section CommRing
 
 variable [CommRing R]
 
-/- warning: polynomial.le_root_multiplicity_iff -> Polynomial.le_rootMultiplicity_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.le_root_multiplicity_iff Polynomial.le_rootMultiplicity_iffₓ'. -/
 /-- The multiplicity of `a` as root of a nonzero polynomial `p` is at least `n` iff
   `(X - a) ^ n` divides `p`. -/
 theorem le_rootMultiplicity_iff {p : R[X]} (p0 : p ≠ 0) {a : R} {n : ℕ} :
@@ -522,27 +393,15 @@ theorem le_rootMultiplicity_iff {p : R[X]} (p0 : p ≠ 0) {a : R} {n : ℕ} :
   cases n; · rw [pow_zero]; apply one_dvd; · exact h n n.lt_succ_self
 #align polynomial.le_root_multiplicity_iff Polynomial.le_rootMultiplicity_iff
 
-/- warning: polynomial.root_multiplicity_le_iff -> Polynomial.rootMultiplicity_le_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.root_multiplicity_le_iff Polynomial.rootMultiplicity_le_iffₓ'. -/
 theorem rootMultiplicity_le_iff {p : R[X]} (p0 : p ≠ 0) (a : R) (n : ℕ) :
     rootMultiplicity a p ≤ n ↔ ¬(X - C a) ^ (n + 1) ∣ p := by
   rw [← (le_root_multiplicity_iff p0).Not, not_le, Nat.lt_add_one_iff]
 #align polynomial.root_multiplicity_le_iff Polynomial.rootMultiplicity_le_iff
 
-/- warning: polynomial.pow_root_multiplicity_not_dvd -> Polynomial.pow_rootMultiplicity_not_dvd is a dubious translation:
-<too large>
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 theorem pow_rootMultiplicity_not_dvd {p : R[X]} (p0 : p ≠ 0) (a : R) :
     ¬(X - C a) ^ (rootMultiplicity a p + 1) ∣ p := by rw [← root_multiplicity_le_iff p0]
 #align polynomial.pow_root_multiplicity_not_dvd Polynomial.pow_rootMultiplicity_not_dvd
 
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 /-- The multiplicity of `p + q` is at least the minimum of the multiplicities. -/
 theorem rootMultiplicity_add {p q : R[X]} (a : R) (hzero : p + q ≠ 0) :
     min (rootMultiplicity a p) (rootMultiplicity a q) ≤ rootMultiplicity a (p + q) :=
@@ -559,12 +418,6 @@ section Roots
 
 open Multiset
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.prime_X_sub_C Polynomial.prime_X_sub_Cₓ'. -/
 theorem prime_X_sub_C (r : R) : Prime (X - C r) :=
   ⟨X_sub_C_ne_zero r, not_isUnit_X_sub_C r, fun _ _ => by
     simp_rw [dvd_iff_is_root, is_root.def, eval_mul, mul_eq_zero]; exact id⟩
@@ -582,42 +435,18 @@ theorem Monic.prime_of_degree_eq_one (hp1 : degree p = 1) (hm : Monic p) : Prime
 #align polynomial.monic.prime_of_degree_eq_one Polynomial.Monic.prime_of_degree_eq_one
 -/
 
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 theorem irreducible_X_sub_C (r : R) : Irreducible (X - C r) :=
   (prime_X_sub_C r).Irreducible
 #align polynomial.irreducible_X_sub_C Polynomial.irreducible_X_sub_C
 
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 theorem irreducible_X : Irreducible (X : R[X]) :=
   Prime.irreducible prime_X
 #align polynomial.irreducible_X Polynomial.irreducible_X
 
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 theorem Monic.irreducible_of_degree_eq_one (hp1 : degree p = 1) (hm : Monic p) : Irreducible p :=
   (hm.prime_of_degree_eq_one hp1).Irreducible
 #align polynomial.monic.irreducible_of_degree_eq_one Polynomial.Monic.irreducible_of_degree_eq_one
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.eq_of_monic_of_associated Polynomial.eq_of_monic_of_associatedₓ'. -/
 theorem eq_of_monic_of_associated (hp : p.Monic) (hq : q.Monic) (hpq : Associated p q) : p = q :=
   by
   obtain ⟨u, hu⟩ := hpq
@@ -640,23 +469,11 @@ theorem rootMultiplicity_mul {p q : R[X]} {x : R} (hpq : p * q ≠ 0) :
 #align polynomial.root_multiplicity_mul Polynomial.rootMultiplicity_mul
 -/
 
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 theorem rootMultiplicity_X_sub_C_self {x : R} : rootMultiplicity x (X - C x) = 1 := by
   rw [root_multiplicity_eq_multiplicity, dif_neg (X_sub_C_ne_zero x),
     multiplicity.get_multiplicity_self]
 #align polynomial.root_multiplicity_X_sub_C_self Polynomial.rootMultiplicity_X_sub_C_self
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.root_multiplicity_X_sub_C Polynomial.rootMultiplicity_X_sub_Cₓ'. -/
 theorem rootMultiplicity_X_sub_C {x y : R} :
     rootMultiplicity x (X - C y) = if x = y then 1 else 0 :=
   by
@@ -666,12 +483,6 @@ theorem rootMultiplicity_X_sub_C {x y : R} :
   exact root_multiplicity_eq_zero (mt root_X_sub_C.mp (Ne.symm hxy))
 #align polynomial.root_multiplicity_X_sub_C Polynomial.rootMultiplicity_X_sub_C
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.root_multiplicity_X_sub_C_pow Polynomial.rootMultiplicity_X_sub_C_powₓ'. -/
 /-- The multiplicity of `a` as root of `(X - a) ^ n` is `n`. -/
 theorem rootMultiplicity_X_sub_C_pow (a : R) (n : ℕ) : rootMultiplicity a ((X - C a) ^ n) = n :=
   by
@@ -683,9 +494,6 @@ theorem rootMultiplicity_X_sub_C_pow (a : R) (n : ℕ) : rootMultiplicity a ((X
   simp only [root_multiplicity_mul hzero, root_multiplicity_X_sub_C_self, hn, Nat.one_add]
 #align polynomial.root_multiplicity_X_sub_C_pow Polynomial.rootMultiplicity_X_sub_C_pow
 
-/- warning: polynomial.exists_multiset_roots -> Polynomial.exists_multiset_roots is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.exists_multiset_roots Polynomial.exists_multiset_rootsₓ'. -/
 theorem exists_multiset_roots :
     ∀ {p : R[X]} (hp : p ≠ 0),
       ∃ s : Multiset R, (s.card : WithBot ℕ) ≤ degree p ∧ ∀ a, s.count a = rootMultiplicity a p
@@ -741,12 +549,6 @@ theorem roots_zero : (0 : R[X]).roots = 0 :=
 #align polynomial.roots_zero Polynomial.roots_zero
 -/
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.card_roots Polynomial.card_rootsₓ'. -/
 theorem card_roots (hp0 : p ≠ 0) : ((roots p).card : WithBot ℕ) ≤ degree p :=
   by
   unfold roots
@@ -754,12 +556,6 @@ theorem card_roots (hp0 : p ≠ 0) : ((roots p).card : WithBot ℕ) ≤ degree p
   exact (Classical.choose_spec (exists_multiset_roots hp0)).1
 #align polynomial.card_roots Polynomial.card_roots
 
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 theorem card_roots' (p : R[X]) : p.roots.card ≤ natDegree p :=
   by
   by_cases hp0 : p = 0
@@ -767,9 +563,6 @@ theorem card_roots' (p : R[X]) : p.roots.card ≤ natDegree p :=
   exact WithBot.coe_le_coe.1 (le_trans (card_roots hp0) (le_of_eq <| degree_eq_nat_degree hp0))
 #align polynomial.card_roots' Polynomial.card_roots'
 
-/- warning: polynomial.card_roots_sub_C -> Polynomial.card_roots_sub_C is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.card_roots_sub_C Polynomial.card_roots_sub_Cₓ'. -/
 theorem card_roots_sub_C {p : R[X]} {a : R} (hp0 : 0 < degree p) :
     ((p - C a).roots.card : WithBot ℕ) ≤ degree p :=
   calc
@@ -779,9 +572,6 @@ theorem card_roots_sub_C {p : R[X]} {a : R} (hp0 : 0 < degree p) :
     
 #align polynomial.card_roots_sub_C Polynomial.card_roots_sub_C
 
-/- warning: polynomial.card_roots_sub_C' -> Polynomial.card_roots_sub_C' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.card_roots_sub_C' Polynomial.card_roots_sub_C'ₓ'. -/
 theorem card_roots_sub_C' {p : R[X]} {a : R} (hp0 : 0 < degree p) :
     (p - C a).roots.card ≤ natDegree p :=
   WithBot.coe_le_coe.1
@@ -844,22 +634,10 @@ theorem eq_zero_of_infinite_isRoot (p : R[X]) (h : Set.Infinite { x | IsRoot p x
 #align polynomial.eq_zero_of_infinite_is_root Polynomial.eq_zero_of_infinite_isRoot
 -/
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.exists_max_root Polynomial.exists_max_rootₓ'. -/
 theorem exists_max_root [LinearOrder R] (p : R[X]) (hp : p ≠ 0) : ∃ x₀, ∀ x, p.IsRoot x → x ≤ x₀ :=
   Set.exists_upper_bound_image _ _ <| finite_setOf_isRoot hp
 #align polynomial.exists_max_root Polynomial.exists_max_root
 
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 theorem exists_min_root [LinearOrder R] (p : R[X]) (hp : p ≠ 0) : ∃ x₀, ∀ x, p.IsRoot x → x₀ ≤ x :=
   Set.exists_lower_bound_image _ _ <| finite_setOf_isRoot hp
 #align polynomial.exists_min_root Polynomial.exists_min_root
@@ -880,42 +658,21 @@ theorem roots_mul {p q : R[X]} (hpq : p * q ≠ 0) : (p * q).roots = p.roots + q
 #align polynomial.roots_mul Polynomial.roots_mul
 -/
 
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 theorem roots.le_of_dvd (h : q ≠ 0) : p ∣ q → roots p ≤ roots q :=
   by
   rintro ⟨k, rfl⟩
   exact multiset.le_iff_exists_add.mpr ⟨k.roots, roots_mul h⟩
 #align polynomial.roots.le_of_dvd Polynomial.roots.le_of_dvd
 
-/- warning: polynomial.mem_roots_sub_C' -> Polynomial.mem_roots_sub_C' is a dubious translation:
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 theorem mem_roots_sub_C' {p : R[X]} {a x : R} : x ∈ (p - C a).roots ↔ p ≠ C a ∧ p.eval x = a := by
   rw [mem_roots', is_root.def, sub_ne_zero, eval_sub, sub_eq_zero, eval_C]
 #align polynomial.mem_roots_sub_C' Polynomial.mem_roots_sub_C'
 
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 theorem mem_roots_sub_C {p : R[X]} {a x : R} (hp0 : 0 < degree p) :
     x ∈ (p - C a).roots ↔ p.eval x = a :=
   mem_roots_sub_C'.trans <| and_iff_right fun hp => hp0.not_le <| hp.symm ▸ degree_C_le
 #align polynomial.mem_roots_sub_C Polynomial.mem_roots_sub_C
 
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 @[simp]
 theorem roots_X_sub_C (r : R) : roots (X - C r) = {r} :=
   by
@@ -923,22 +680,10 @@ theorem roots_X_sub_C (r : R) : roots (X - C r) = {r} :=
   rw [count_roots, root_multiplicity_X_sub_C, count_singleton]
 #align polynomial.roots_X_sub_C Polynomial.roots_X_sub_C
 
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 @[simp]
 theorem roots_X : roots (X : R[X]) = {0} := by rw [← roots_X_sub_C, C_0, sub_zero]
 #align polynomial.roots_X Polynomial.roots_X
 
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 @[simp]
 theorem roots_C (x : R) : (C x).roots = 0 :=
   if H : x = 0 then by rw [H, C_0, roots_zero]
@@ -954,12 +699,6 @@ theorem roots_one : (1 : R[X]).roots = ∅ :=
 #align polynomial.roots_one Polynomial.roots_one
 -/
 
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 @[simp]
 theorem roots_C_mul (p : R[X]) (ha : a ≠ 0) : (C a * p).roots = p.roots := by
   by_cases hp : p = 0 <;>
@@ -967,12 +706,6 @@ theorem roots_C_mul (p : R[X]) (ha : a ≠ 0) : (C a * p).roots = p.roots := by
       zero_add, MulZeroClass.mul_zero]
 #align polynomial.roots_C_mul Polynomial.roots_C_mul
 
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 @[simp]
 theorem roots_smul_nonzero (p : R[X]) (ha : a ≠ 0) : (a • p).roots = p.roots := by
   rw [smul_eq_C_mul, roots_C_mul _ ha]
@@ -995,12 +728,6 @@ theorem roots_multiset_prod (m : Multiset R[X]) : (0 : R[X]) ∉ m → m.Prod.ro
 #align polynomial.roots_multiset_prod Polynomial.roots_multiset_prod
 -/
 
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 theorem roots_prod {ι : Type _} (f : ι → R[X]) (s : Finset ι) :
     s.Prod f ≠ 0 → (s.Prod f).roots = s.val.bind fun i => roots (f i) :=
   by
@@ -1008,12 +735,6 @@ theorem roots_prod {ι : Type _} (f : ι → R[X]) (s : Finset ι) :
   simpa [Multiset.prod_eq_zero_iff, bind_map] using roots_multiset_prod (m.map f)
 #align polynomial.roots_prod Polynomial.roots_prod
 
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 @[simp]
 theorem roots_pow (p : R[X]) (n : ℕ) : (p ^ n).roots = n • p.roots :=
   by
@@ -1026,47 +747,23 @@ theorem roots_pow (p : R[X]) (n : ℕ) : (p ^ n).roots = n • p.roots :=
         add_smul, one_smul]
 #align polynomial.roots_pow Polynomial.roots_pow
 
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 theorem roots_X_pow (n : ℕ) : (X ^ n : R[X]).roots = n • {0} := by rw [roots_pow, roots_X]
 #align polynomial.roots_X_pow Polynomial.roots_X_pow
 
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 theorem roots_C_mul_X_pow (ha : a ≠ 0) (n : ℕ) : (C a * X ^ n).roots = n • {0} := by
   rw [roots_C_mul _ ha, roots_X_pow]
 #align polynomial.roots_C_mul_X_pow Polynomial.roots_C_mul_X_pow
 
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 @[simp]
 theorem roots_monomial (ha : a ≠ 0) (n : ℕ) : (monomial n a).roots = n • {0} := by
   rw [← C_mul_X_pow_eq_monomial, roots_C_mul_X_pow ha]
 #align polynomial.roots_monomial Polynomial.roots_monomial
 
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 theorem roots_prod_X_sub_C (s : Finset R) : (s.Prod fun a => X - C a).roots = s.val :=
   (roots_prod (fun a => X - C a) s (prod_ne_zero_iff.mpr fun a _ => X_sub_C_ne_zero a)).trans
     (by simp_rw [roots_X_sub_C, Multiset.bind_singleton, Multiset.map_id'])
 #align polynomial.roots_prod_X_sub_C Polynomial.roots_prod_X_sub_C
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.roots_multiset_prod_X_sub_C Polynomial.roots_multiset_prod_X_sub_Cₓ'. -/
 @[simp]
 theorem roots_multiset_prod_X_sub_C (s : Multiset R) : (s.map fun a => X - C a).Prod.roots = s :=
   by
@@ -1075,9 +772,6 @@ theorem roots_multiset_prod_X_sub_C (s : Multiset R) : (s.map fun a => X - C a).
   · rw [Multiset.mem_map]; rintro ⟨a, -, h⟩; exact X_sub_C_ne_zero a h
 #align polynomial.roots_multiset_prod_X_sub_C Polynomial.roots_multiset_prod_X_sub_C
 
-/- warning: polynomial.nat_degree_multiset_prod_X_sub_C_eq_card -> Polynomial.natDegree_multiset_prod_X_sub_C_eq_card is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_multiset_prod_X_sub_C_eq_card Polynomial.natDegree_multiset_prod_X_sub_C_eq_cardₓ'. -/
 @[simp]
 theorem natDegree_multiset_prod_X_sub_C_eq_card (s : Multiset R) :
     (s.map fun a => X - C a).Prod.natDegree = s.card :=
@@ -1089,9 +783,6 @@ theorem natDegree_multiset_prod_X_sub_C_eq_card (s : Multiset R) :
   · exact Multiset.forall_mem_map_iff.2 fun a _ => monic_X_sub_C a
 #align polynomial.nat_degree_multiset_prod_X_sub_C_eq_card Polynomial.natDegree_multiset_prod_X_sub_C_eq_card
 
-/- warning: polynomial.card_roots_X_pow_sub_C -> Polynomial.card_roots_X_pow_sub_C is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.card_roots_X_pow_sub_C Polynomial.card_roots_X_pow_sub_Cₓ'. -/
 theorem card_roots_X_pow_sub_C {n : ℕ} (hn : 0 < n) (a : R) :
     (roots ((X : R[X]) ^ n - C a)).card ≤ n :=
   WithBot.coe_le_coe.1 <|
@@ -1111,12 +802,6 @@ def nthRoots (n : ℕ) (a : R) : Multiset R :=
 #align polynomial.nth_roots Polynomial.nthRoots
 -/
 
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 @[simp]
 theorem mem_nthRoots {n : ℕ} (hn : 0 < n) {a x : R} : x ∈ nthRoots n a ↔ x ^ n = a := by
   rw [nth_roots, mem_roots (X_pow_sub_C_ne_zero hn a), is_root.def, eval_sub, eval_C, eval_pow,
@@ -1130,12 +815,6 @@ theorem nthRoots_zero (r : R) : nthRoots 0 r = 0 := by
 #align polynomial.nth_roots_zero Polynomial.nthRoots_zero
 -/
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.card_nth_roots Polynomial.card_nthRootsₓ'. -/
 theorem card_nthRoots (n : ℕ) (a : R) : (nthRoots n a).card ≤ n :=
   if hn : n = 0 then
     if h : (X : R[X]) ^ n - C a = 0 then by
@@ -1151,12 +830,6 @@ theorem card_nthRoots (n : ℕ) (a : R) : (nthRoots n a).card ≤ n :=
       exact card_roots (X_pow_sub_C_ne_zero (Nat.pos_of_ne_zero hn) a)
 #align polynomial.card_nth_roots Polynomial.card_nthRoots
 
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 @[simp]
 theorem nthRoots_two_eq_zero_iff {r : R} : nthRoots 2 r = 0 ↔ ¬IsSquare r := by
   simp_rw [isSquare_iff_exists_sq, eq_zero_iff_forall_not_mem, mem_nth_roots (by norm_num : 0 < 2),
@@ -1170,12 +843,6 @@ def nthRootsFinset (n : ℕ) (R : Type _) [CommRing R] [IsDomain R] : Finset R :
 #align polynomial.nth_roots_finset Polynomial.nthRootsFinset
 -/
 
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 @[simp]
 theorem mem_nthRootsFinset {n : ℕ} (h : 0 < n) {x : R} : x ∈ nthRootsFinset n R ↔ x ^ (n : ℕ) = 1 :=
   by rw [nth_roots_finset, mem_to_finset, mem_nth_roots h]
@@ -1195,12 +862,6 @@ theorem Monic.comp (hp : p.Monic) (hq : q.Monic) (h : q.natDegree ≠ 0) : (p.co
 #align polynomial.monic.comp Polynomial.Monic.comp
 -/
 
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 theorem Monic.comp_X_add_C (hp : p.Monic) (r : R) : (p.comp (X + C r)).Monic :=
   by
   refine' hp.comp (monic_X_add_C _) fun ha => _
@@ -1208,40 +869,19 @@ theorem Monic.comp_X_add_C (hp : p.Monic) (r : R) : (p.comp (X + C r)).Monic :=
   exact one_ne_zero ha
 #align polynomial.monic.comp_X_add_C Polynomial.Monic.comp_X_add_C
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.monic.comp_X_sub_C Polynomial.Monic.comp_X_sub_Cₓ'. -/
 theorem Monic.comp_X_sub_C (hp : p.Monic) (r : R) : (p.comp (X - C r)).Monic := by
   simpa using hp.comp_X_add_C (-r)
 #align polynomial.monic.comp_X_sub_C Polynomial.Monic.comp_X_sub_C
 
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 theorem units_coeff_zero_smul (c : R[X]ˣ) (p : R[X]) : (c : R[X]).coeff 0 • p = c * p := by
   rw [← Polynomial.C_mul', ← Polynomial.eq_C_of_degree_eq_zero (degree_coe_units c)]
 #align polynomial.units_coeff_zero_smul Polynomial.units_coeff_zero_smul
 
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 @[simp]
 theorem natDegree_coe_units (u : R[X]ˣ) : natDegree (u : R[X]) = 0 :=
   natDegree_eq_of_degree_eq_some (degree_coe_units u)
 #align polynomial.nat_degree_coe_units Polynomial.natDegree_coe_units
 
-/- warning: polynomial.comp_eq_zero_iff -> Polynomial.comp_eq_zero_iff is a dubious translation:
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 theorem comp_eq_zero_iff : p.comp q = 0 ↔ p = 0 ∨ p.eval (q.coeff 0) = 0 ∧ q = C (q.coeff 0) :=
   by
   constructor
@@ -1259,12 +899,6 @@ theorem comp_eq_zero_iff : p.comp q = 0 ↔ p = 0 ∨ p.eval (q.coeff 0) = 0 ∧
       Or.ndrec (fun h => by rw [h, zero_comp]) (fun h => by rw [h.2, comp_C, h.1, C_0]) h
 #align polynomial.comp_eq_zero_iff Polynomial.comp_eq_zero_iff
 
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 theorem zero_of_eval_zero [Infinite R] (p : R[X]) (h : ∀ x, p.eval x = 0) : p = 0 := by
   classical by_contra hp <;>
       exact
@@ -1294,31 +928,16 @@ def rootSet (p : T[X]) (S) [CommRing S] [IsDomain S] [Algebra T S] : Set S :=
 #align polynomial.root_set Polynomial.rootSet
 -/
 
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 theorem rootSet_def (p : T[X]) (S) [CommRing S] [IsDomain S] [Algebra T S] :
     p.rootSet S = (p.map (algebraMap T S)).roots.toFinset :=
   rfl
 #align polynomial.root_set_def Polynomial.rootSet_def
 
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 @[simp]
 theorem rootSet_C [CommRing S] [IsDomain S] [Algebra T S] (a : T) : (C a).rootSet S = ∅ := by
   rw [root_set_def, map_C, roots_C, Multiset.toFinset_zero, Finset.coe_empty]
 #align polynomial.root_set_C Polynomial.rootSet_C
 
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 @[simp]
 theorem rootSet_zero (S) [CommRing S] [IsDomain S] [Algebra T S] : (0 : T[X]).rootSet S = ∅ := by
   rw [← C_0, root_set_C]
@@ -1331,23 +950,11 @@ instance rootSetFintype (p : T[X]) (S : Type _) [CommRing S] [IsDomain S] [Algeb
 #align polynomial.root_set_fintype Polynomial.rootSetFintype
 -/
 
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 theorem rootSet_finite (p : T[X]) (S : Type _) [CommRing S] [IsDomain S] [Algebra T S] :
     (p.rootSet S).Finite :=
   Set.toFinite _
 #align polynomial.root_set_finite Polynomial.rootSet_finite
 
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 /-- The set of roots of all polynomials of bounded degree and having coefficients in a finite set
 is finite. -/
 theorem bUnion_roots_finite {R S : Type _} [Semiring R] [CommRing S] [IsDomain S] (m : R →+* S)
@@ -1366,35 +973,23 @@ theorem bUnion_roots_finite {R S : Type _} [Semiring R] [CommRing S] [IsDomain S
     fun i hi => Finset.finite_toSet _
 #align polynomial.bUnion_roots_finite Polynomial.bUnion_roots_finite
 
-/- warning: polynomial.mem_root_set' -> Polynomial.mem_rootSet' is a dubious translation:
-<too large>
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 theorem mem_rootSet' {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Algebra T S] {a : S} :
     a ∈ p.rootSet S ↔ p.map (algebraMap T S) ≠ 0 ∧ aeval a p = 0 := by
   rw [root_set, Finset.mem_coe, mem_to_finset, mem_roots', is_root.def, ← eval₂_eq_eval_map,
     aeval_def]
 #align polynomial.mem_root_set' Polynomial.mem_rootSet'
 
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-<too large>
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 theorem mem_rootSet {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Algebra T S]
     [NoZeroSMulDivisors T S] {a : S} : a ∈ p.rootSet S ↔ p ≠ 0 ∧ aeval a p = 0 := by
   rw [mem_root_set',
     (map_injective _ (NoZeroSMulDivisors.algebraMap_injective T S)).ne_iff' (Polynomial.map_zero _)]
 #align polynomial.mem_root_set Polynomial.mem_rootSet
 
-/- warning: polynomial.mem_root_set_of_ne -> Polynomial.mem_rootSet_of_ne is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.mem_root_set_of_ne Polynomial.mem_rootSet_of_neₓ'. -/
 theorem mem_rootSet_of_ne {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Algebra T S]
     [NoZeroSMulDivisors T S] (hp : p ≠ 0) {a : S} : a ∈ p.rootSet S ↔ aeval a p = 0 :=
   mem_rootSet.trans <| and_iff_right hp
 #align polynomial.mem_root_set_of_ne Polynomial.mem_rootSet_of_ne
 
-/- warning: polynomial.root_set_maps_to' -> Polynomial.rootSet_maps_to' is a dubious translation:
-<too large>
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 theorem rootSet_maps_to' {p : T[X]} {S S'} [CommRing S] [IsDomain S] [Algebra T S] [CommRing S']
     [IsDomain S'] [Algebra T S'] (hp : p.map (algebraMap T S') = 0 → p.map (algebraMap T S) = 0)
     (f : S →ₐ[T] S') : (p.rootSet S).MapsTo f (p.rootSet S') := fun x hx =>
@@ -1417,9 +1012,6 @@ theorem aeval_eq_zero_of_mem_rootSet {p : T[X]} [CommRing S] [IsDomain S] [Algeb
 #align polynomial.aeval_eq_zero_of_mem_root_set Polynomial.aeval_eq_zero_of_mem_rootSet
 -/
 
-/- warning: polynomial.root_set_maps_to -> Polynomial.rootSet_mapsTo is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.root_set_maps_to Polynomial.rootSet_mapsToₓ'. -/
 theorem rootSet_mapsTo {p : T[X]} {S S'} [CommRing S] [IsDomain S] [Algebra T S] [CommRing S']
     [IsDomain S'] [Algebra T S'] [NoZeroSMulDivisors T S'] (f : S →ₐ[T] S') :
     (p.rootSet S).MapsTo f (p.rootSet S') :=
@@ -1432,12 +1024,6 @@ theorem rootSet_mapsTo {p : T[X]} {S S'} [CommRing S] [IsDomain S] [Algebra T S]
 
 end Roots
 
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 theorem coeff_coe_units_zero_ne_zero (u : R[X]ˣ) : coeff (u : R[X]) 0 ≠ 0 :=
   by
   conv in 0 => rw [← nat_degree_coe_units u]
@@ -1445,24 +1031,12 @@ theorem coeff_coe_units_zero_ne_zero (u : R[X]ˣ) : coeff (u : R[X]) 0 ≠ 0 :=
   exact Units.ne_zero _
 #align polynomial.coeff_coe_units_zero_ne_zero Polynomial.coeff_coe_units_zero_ne_zero
 
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 theorem degree_eq_degree_of_associated (h : Associated p q) : degree p = degree q :=
   by
   let ⟨u, hu⟩ := h
   simp [hu.symm]
 #align polynomial.degree_eq_degree_of_associated Polynomial.degree_eq_degree_of_associated
 
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 theorem degree_eq_one_of_irreducible_of_root (hi : Irreducible p) {x : R} (hx : IsRoot p x) :
     degree p = 1 :=
   let ⟨g, hg⟩ := dvd_iff_isRoot.2 hx
@@ -1475,12 +1049,6 @@ theorem degree_eq_one_of_irreducible_of_root (hi : Irreducible p) {x : R} (hx :
     fun hgu => by rw [hg, degree_mul, degree_X_sub_C, degree_eq_zero_of_is_unit hgu, add_zero]
 #align polynomial.degree_eq_one_of_irreducible_of_root Polynomial.degree_eq_one_of_irreducible_of_root
 
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 /-- Division by a monic polynomial doesn't change the leading coefficient. -/
 theorem leadingCoeff_divByMonic_of_monic {R : Type u} [CommRing R] {p q : R[X]} (hmonic : q.Monic)
     (hdegree : q.degree ≤ p.degree) : (p /ₘ q).leadingCoeff = p.leadingCoeff :=
@@ -1495,12 +1063,6 @@ theorem leadingCoeff_divByMonic_of_monic {R : Type u} [CommRing R] {p q : R[X]}
   exact (degree_mod_by_monic_lt p hmonic).trans_le hdegree
 #align polynomial.leading_coeff_div_by_monic_of_monic Polynomial.leadingCoeff_divByMonic_of_monic
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.leading_coeff_div_by_monic_X_sub_C Polynomial.leadingCoeff_divByMonic_X_sub_Cₓ'. -/
 theorem leadingCoeff_divByMonic_X_sub_C (p : R[X]) (hp : degree p ≠ 0) (a : R) :
     leadingCoeff (p /ₘ (X - C a)) = leadingCoeff p :=
   by
@@ -1511,9 +1073,6 @@ theorem leadingCoeff_divByMonic_X_sub_C (p : R[X]) (hp : degree p ≠ 0) (a : R)
   rwa [degree_X_sub_C, Nat.WithBot.one_le_iff_zero_lt]
 #align polynomial.leading_coeff_div_by_monic_X_sub_C Polynomial.leadingCoeff_divByMonic_X_sub_C
 
-/- warning: polynomial.eq_leading_coeff_mul_of_monic_of_dvd_of_nat_degree_le -> Polynomial.eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.eq_leading_coeff_mul_of_monic_of_dvd_of_nat_degree_le Polynomial.eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_leₓ'. -/
 theorem eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le {R} [CommRing R] {p q : R[X]}
     (hp : p.Monic) (hdiv : p ∣ q) (hdeg : q.natDegree ≤ p.natDegree) : q = C q.leadingCoeff * p :=
   by
@@ -1536,9 +1095,6 @@ theorem eq_of_monic_of_dvd_of_natDegree_le {R} [CommRing R] {p q : R[X]} (hp : p
 #align polynomial.eq_of_monic_of_dvd_of_nat_degree_le Polynomial.eq_of_monic_of_dvd_of_natDegree_le
 -/
 
-/- warning: polynomial.is_coprime_X_sub_C_of_is_unit_sub -> Polynomial.isCoprime_X_sub_C_of_isUnit_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.is_coprime_X_sub_C_of_is_unit_sub Polynomial.isCoprime_X_sub_C_of_isUnit_subₓ'. -/
 theorem isCoprime_X_sub_C_of_isUnit_sub {R} [CommRing R] {a b : R} (h : IsUnit (a - b)) :
     IsCoprime (X - C a) (X - C b) :=
   ⟨-C h.Unit⁻¹.val, C h.Unit⁻¹.val,
@@ -1547,36 +1103,21 @@ theorem isCoprime_X_sub_C_of_isUnit_sub {R} [CommRing R] {a b : R} (h : IsUnit (
     convert C_1; exact h.coe_inv_mul⟩
 #align polynomial.is_coprime_X_sub_C_of_is_unit_sub Polynomial.isCoprime_X_sub_C_of_isUnit_sub
 
-/- warning: polynomial.pairwise_coprime_X_sub_C -> Polynomial.pairwise_coprime_X_sub_C is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.pairwise_coprime_X_sub_C Polynomial.pairwise_coprime_X_sub_Cₓ'. -/
 theorem pairwise_coprime_X_sub_C {K} [Field K] {I : Type v} {s : I → K} (H : Function.Injective s) :
     Pairwise (IsCoprime on fun i : I => X - C (s i)) := fun i j hij =>
   isCoprime_X_sub_C_of_isUnit_sub (sub_ne_zero_of_ne <| H.Ne hij).IsUnit
 #align polynomial.pairwise_coprime_X_sub_C Polynomial.pairwise_coprime_X_sub_C
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.monic_prod_multiset_X_sub_C Polynomial.monic_prod_multiset_X_sub_Cₓ'. -/
 theorem monic_prod_multiset_X_sub_C : Monic (p.roots.map fun a => X - C a).Prod :=
   monic_multiset_prod_of_monic _ _ fun a _ => monic_X_sub_C a
 #align polynomial.monic_prod_multiset_X_sub_C Polynomial.monic_prod_multiset_X_sub_C
 
-/- warning: polynomial.prod_multiset_root_eq_finset_root -> Polynomial.prod_multiset_root_eq_finset_root is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.prod_multiset_root_eq_finset_root Polynomial.prod_multiset_root_eq_finset_rootₓ'. -/
 theorem prod_multiset_root_eq_finset_root :
     (p.roots.map fun a => X - C a).Prod =
       p.roots.toFinset.Prod fun a => (X - C a) ^ rootMultiplicity a p :=
   by simp only [count_roots, Finset.prod_multiset_map_count]
 #align polynomial.prod_multiset_root_eq_finset_root Polynomial.prod_multiset_root_eq_finset_root
 
-/- warning: polynomial.prod_multiset_X_sub_C_dvd -> Polynomial.prod_multiset_X_sub_C_dvd is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.prod_multiset_X_sub_C_dvd Polynomial.prod_multiset_X_sub_C_dvdₓ'. -/
 /-- The product `∏ (X - a)` for `a` inside the multiset `p.roots` divides `p`. -/
 theorem prod_multiset_X_sub_C_dvd (p : R[X]) : (p.roots.map fun a => X - C a).Prod ∣ p :=
   by
@@ -1588,9 +1129,6 @@ theorem prod_multiset_X_sub_C_dvd (p : R[X]) : (p.roots.map fun a => X - C a).Pr
   · exact Polynomial.map_dvd _ (pow_root_multiplicity_dvd p a)
 #align polynomial.prod_multiset_X_sub_C_dvd Polynomial.prod_multiset_X_sub_C_dvd
 
-/- warning: multiset.prod_X_sub_C_dvd_iff_le_roots -> Multiset.prod_X_sub_C_dvd_iff_le_roots is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align multiset.prod_X_sub_C_dvd_iff_le_roots Multiset.prod_X_sub_C_dvd_iff_le_rootsₓ'. -/
 /-- A Galois connection. -/
 theorem Multiset.prod_X_sub_C_dvd_iff_le_roots {p : R[X]} (hp : p ≠ 0) (s : Multiset R) :
     (s.map fun a => X - C a).Prod ∣ p ↔ s ≤ p.roots :=
@@ -1604,9 +1142,6 @@ theorem Multiset.prod_X_sub_C_dvd_iff_le_roots {p : R[X]} (hp : p ≠ 0) (s : Mu
     (Multiset.prod_dvd_prod_of_le <| Multiset.map_le_map h).trans p.prod_multiset_X_sub_C_dvd⟩
 #align multiset.prod_X_sub_C_dvd_iff_le_roots Multiset.prod_X_sub_C_dvd_iff_le_roots
 
-/- warning: polynomial.exists_prod_multiset_X_sub_C_mul -> Polynomial.exists_prod_multiset_X_sub_C_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.exists_prod_multiset_X_sub_C_mul Polynomial.exists_prod_multiset_X_sub_C_mulₓ'. -/
 theorem exists_prod_multiset_X_sub_C_mul (p : R[X]) :
     ∃ q,
       (p.roots.map fun a => X - C a).Prod * q = p ∧
@@ -1624,9 +1159,6 @@ theorem exists_prod_multiset_X_sub_C_mul (p : R[X]) :
     exacts[add_right_eq_self.1 he, mul_ne_zero monic_prod_multiset_X_sub_C.ne_zero hq]
 #align polynomial.exists_prod_multiset_X_sub_C_mul Polynomial.exists_prod_multiset_X_sub_C_mul
 
-/- warning: polynomial.C_leading_coeff_mul_prod_multiset_X_sub_C -> Polynomial.C_leadingCoeff_mul_prod_multiset_X_sub_C is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.C_leading_coeff_mul_prod_multiset_X_sub_C Polynomial.C_leadingCoeff_mul_prod_multiset_X_sub_Cₓ'. -/
 /-- A polynomial `p` that has as many roots as its degree
 can be written `p = p.leading_coeff * ∏(X - a)`, for `a` in `p.roots`. -/
 theorem C_leadingCoeff_mul_prod_multiset_X_sub_C (hroots : p.roots.card = p.natDegree) :
@@ -1636,9 +1168,6 @@ theorem C_leadingCoeff_mul_prod_multiset_X_sub_C (hroots : p.roots.card = p.natD
       ((natDegree_multiset_prod_X_sub_C_eq_card _).trans hroots).ge).symm
 #align polynomial.C_leading_coeff_mul_prod_multiset_X_sub_C Polynomial.C_leadingCoeff_mul_prod_multiset_X_sub_C
 
-/- warning: polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq -> Polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq Polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eqₓ'. -/
 /-- A monic polynomial `p` that has as many roots as its degree
 can be written `p = ∏(X - a)`, for `a` in `p.roots`. -/
 theorem prod_multiset_X_sub_C_of_monic_of_roots_card_eq (hp : p.Monic)
@@ -1652,12 +1181,6 @@ section
 
 variable {A B : Type _} [CommRing A] [CommRing B]
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.le_root_multiplicity_map Polynomial.le_rootMultiplicity_mapₓ'. -/
 theorem le_rootMultiplicity_map {p : A[X]} {f : A →+* B} (hmap : map f p ≠ 0) (a : A) :
     rootMultiplicity a p ≤ rootMultiplicity (f a) (p.map f) :=
   by
@@ -1666,12 +1189,6 @@ theorem le_rootMultiplicity_map {p : A[X]} {f : A →+* B} (hmap : map f p ≠ 0
   rw [map_pow, map_sub, coe_map_ring_hom, map_X, map_C]
 #align polynomial.le_root_multiplicity_map Polynomial.le_rootMultiplicity_map
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.eq_root_multiplicity_map Polynomial.eq_rootMultiplicity_mapₓ'. -/
 theorem eq_rootMultiplicity_map {p : A[X]} {f : A →+* B} (hf : Function.Injective f) (a : A) :
     rootMultiplicity a p = rootMultiplicity (f a) (p.map f) :=
   by
@@ -1682,12 +1199,6 @@ theorem eq_rootMultiplicity_map {p : A[X]} {f : A →+* B} (hf : Function.Inject
   apply pow_root_multiplicity_dvd
 #align polynomial.eq_root_multiplicity_map Polynomial.eq_rootMultiplicity_map
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.count_map_roots Polynomial.count_map_rootsₓ'. -/
 theorem count_map_roots [IsDomain A] {p : A[X]} {f : A →+* B} (hmap : map f p ≠ 0) (b : B) :
     (p.roots.map f).count b ≤ rootMultiplicity b (p.map f) :=
   by
@@ -1701,12 +1212,6 @@ theorem count_map_roots [IsDomain A] {p : A[X]} {f : A →+* B} (hmap : map f p
   simp only [Function.comp_apply, Polynomial.map_sub, map_X, map_C]
 #align polynomial.count_map_roots Polynomial.count_map_roots
 
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 theorem count_map_roots_of_injective [IsDomain A] (p : A[X]) {f : A →+* B}
     (hf : Function.Injective f) (b : B) : (p.roots.map f).count b ≤ rootMultiplicity b (p.map f) :=
   by
@@ -1717,23 +1222,11 @@ theorem count_map_roots_of_injective [IsDomain A] (p : A[X]) {f : A →+* B}
   · exact count_map_roots ((Polynomial.map_ne_zero_iff hf).mpr hp0) b
 #align polynomial.count_map_roots_of_injective Polynomial.count_map_roots_of_injective
 
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 theorem map_roots_le [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (h : p.map f ≠ 0) :
     p.roots.map f ≤ (p.map f).roots :=
   Multiset.le_iff_count.2 fun b => by rw [count_roots]; apply count_map_roots h
 #align polynomial.map_roots_le Polynomial.map_roots_le
 
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_inst_2))))))) f) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (Polynomial.roots.{u1} B _inst_2 _inst_4 (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p)))
-Case conversion may be inaccurate. Consider using '#align polynomial.map_roots_le_of_injective Polynomial.map_roots_le_of_injectiveₓ'. -/
 theorem map_roots_le_of_injective [IsDomain A] [IsDomain B] (p : A[X]) {f : A →+* B}
     (hf : Function.Injective f) : p.roots.map f ≤ (p.map f).roots :=
   by
@@ -1741,17 +1234,11 @@ theorem map_roots_le_of_injective [IsDomain A] [IsDomain B] (p : A[X]) {f : A 
   exact map_roots_le ((Polynomial.map_ne_zero_iff hf).mpr hp0)
 #align polynomial.map_roots_le_of_injective Polynomial.map_roots_le_of_injective
 
-/- warning: polynomial.card_roots_le_map -> Polynomial.card_roots_le_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.card_roots_le_map Polynomial.card_roots_le_mapₓ'. -/
 theorem card_roots_le_map [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (h : p.map f ≠ 0) :
     p.roots.card ≤ (p.map f).roots.card := by rw [← p.roots.card_map f];
   exact Multiset.card_le_of_le (map_roots_le h)
 #align polynomial.card_roots_le_map Polynomial.card_roots_le_map
 
-/- warning: polynomial.card_roots_le_map_of_injective -> Polynomial.card_roots_le_map_of_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.card_roots_le_map_of_injective Polynomial.card_roots_le_map_of_injectiveₓ'. -/
 theorem card_roots_le_map_of_injective [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B}
     (hf : Function.Injective f) : p.roots.card ≤ (p.map f).roots.card :=
   by
@@ -1759,9 +1246,6 @@ theorem card_roots_le_map_of_injective [IsDomain A] [IsDomain B] {p : A[X]} {f :
   exact card_roots_le_map ((Polynomial.map_ne_zero_iff hf).mpr hp0)
 #align polynomial.card_roots_le_map_of_injective Polynomial.card_roots_le_map_of_injective
 
-/- warning: polynomial.roots_map_of_injective_of_card_eq_nat_degree -> Polynomial.roots_map_of_injective_of_card_eq_natDegree is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.roots_map_of_injective_of_card_eq_nat_degree Polynomial.roots_map_of_injective_of_card_eq_natDegreeₓ'. -/
 theorem roots_map_of_injective_of_card_eq_natDegree [IsDomain A] [IsDomain B] {p : A[X]}
     {f : A →+* B} (hf : Function.Injective f) (hroots : p.roots.card = p.natDegree) :
     p.roots.map f = (p.map f).roots :=
@@ -1776,12 +1260,6 @@ section
 
 variable [Semiring R] [CommRing S] [IsDomain S] (φ : R →+* S)
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.is_unit_of_is_unit_leading_coeff_of_is_unit_map Polynomial.isUnit_of_isUnit_leadingCoeff_of_isUnit_mapₓ'. -/
 theorem isUnit_of_isUnit_leadingCoeff_of_isUnit_map {f : R[X]} (hf : IsUnit f.leadingCoeff)
     (H : IsUnit (map φ f)) : IsUnit f :=
   by
@@ -1805,12 +1283,6 @@ section
 
 variable [CommRing R] [IsDomain R] [CommRing S] [IsDomain S] (φ : R →+* S)
 
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-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : CommRing.{u2} S] [_inst_4 : IsDomain.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_3))] (φ : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_3)))) (f : 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)) f) -> (Irreducible.{u2} (Polynomial.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_3))) (MonoidWithZero.toMonoid.{u2} (Polynomial.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_3))) (Semiring.toMonoidWithZero.{u2} (Polynomial.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_3))) (Polynomial.semiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_3))))) (Polynomial.map.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_3)) φ f)) -> (Irreducible.{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))) (Semiring.toMonoidWithZero.{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))))) f)
-Case conversion may be inaccurate. Consider using '#align polynomial.monic.irreducible_of_irreducible_map Polynomial.Monic.irreducible_of_irreducible_mapₓ'. -/
 /-- A polynomial over an integral domain `R` is irreducible if it is monic and
   irreducible after mapping into an integral domain `S`.
 

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

@@ -462,8 +462,7 @@ theorem Monic.not_irreducible_iff_exists_add_mul_eq_coeff (hm : p.Monic) (hnd :
   rw [hm.irreducible_iff_nat_degree', and_iff_right, hnd]
   push_neg; constructor
   · rintro ⟨a, b, ha, hb, rfl, hdb | ⟨⟨⟩⟩⟩
-    have hda := hnd
-    rw [ha.nat_degree_mul hb, hdb] at hda
+    have hda := hnd; rw [ha.nat_degree_mul hb, hdb] at hda
     use a.coeff 0, b.coeff 0, mul_coeff_zero a b
     simpa only [next_coeff, hnd, add_right_cancel hda, hdb] using ha.next_coeff_mul hb
   · rintro ⟨c₁, c₂, hmul, hadd⟩
@@ -472,8 +471,7 @@ theorem Monic.not_irreducible_iff_exists_add_mul_eq_coeff (hm : p.Monic) (hnd :
     rw [p.as_sum_range_C_mul_X_pow, hnd, Finset.sum_range_succ, Finset.sum_range_succ,
       Finset.sum_range_one, ← hnd, hm.coeff_nat_degree, hnd, hmul, hadd, C_mul, C_add, C_1]
     ring
-  · rintro rfl
-    simpa only [nat_degree_one] using hnd
+  · rintro rfl; simpa only [nat_degree_one] using hnd
 #align polynomial.monic.not_irreducible_iff_exists_add_mul_eq_coeff Polynomial.Monic.not_irreducible_iff_exists_add_mul_eq_coeff
 
 /- warning: polynomial.root_mul -> Polynomial.root_mul is a dubious translation:
@@ -521,9 +519,7 @@ theorem le_rootMultiplicity_iff {p : R[X]} (p0 : p ≠ 0) {a : R} {n : ℕ} :
   by
   simp_rw [root_multiplicity, dif_neg p0, Nat.le_find_iff, Classical.not_not]
   refine' ⟨fun h => _, fun h m hm => (pow_dvd_pow _ hm).trans h⟩
-  cases n;
-  · rw [pow_zero]
-    apply one_dvd; · exact h n n.lt_succ_self
+  cases n; · rw [pow_zero]; apply one_dvd; · exact h n n.lt_succ_self
 #align polynomial.le_root_multiplicity_iff Polynomial.le_rootMultiplicity_iff
 
 /- warning: polynomial.root_multiplicity_le_iff -> Polynomial.rootMultiplicity_le_iff is a dubious translation:
@@ -570,17 +566,12 @@ 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))] (r : R), Prime.{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))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{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))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) r))
 Case conversion may be inaccurate. Consider using '#align polynomial.prime_X_sub_C Polynomial.prime_X_sub_Cₓ'. -/
 theorem prime_X_sub_C (r : R) : Prime (X - C r) :=
-  ⟨X_sub_C_ne_zero r, not_isUnit_X_sub_C r, fun _ _ =>
-    by
-    simp_rw [dvd_iff_is_root, is_root.def, eval_mul, mul_eq_zero]
-    exact id⟩
+  ⟨X_sub_C_ne_zero r, not_isUnit_X_sub_C r, fun _ _ => by
+    simp_rw [dvd_iff_is_root, is_root.def, eval_mul, mul_eq_zero]; exact id⟩
 #align polynomial.prime_X_sub_C Polynomial.prime_X_sub_C
 
 #print Polynomial.prime_X /-
-theorem prime_X : Prime (X : R[X]) :=
-  by
-  convert prime_X_sub_C (0 : R)
-  simp
+theorem prime_X : Prime (X : R[X]) := by convert prime_X_sub_C (0 : R); simp
 #align polynomial.prime_X Polynomial.prime_X
 -/
 
@@ -731,9 +722,7 @@ theorem exists_multiset_roots :
         · rw [ha, count_cons_self, Nat.succ_eq_add_one, add_comm]
         · rw [count_cons_of_ne ha, zero_add]⟩
     else
-      ⟨0, (degree_eq_nat_degree hp).symm ▸ WithBot.coe_le_coe.2 (Nat.zero_le _),
-        by
-        intro a
+      ⟨0, (degree_eq_nat_degree hp).symm ▸ WithBot.coe_le_coe.2 (Nat.zero_le _), by intro a;
         rw [count_zero, root_multiplicity_eq_zero (not_exists.mp h a)]⟩
 #align polynomial.exists_multiset_roots Polynomial.exists_multiset_roots
 
@@ -1001,10 +990,8 @@ theorem roots_list_prod (L : List R[X]) :
 -/
 
 #print Polynomial.roots_multiset_prod /-
-theorem roots_multiset_prod (m : Multiset R[X]) : (0 : R[X]) ∉ m → m.Prod.roots = m.bind roots :=
-  by
-  rcases m with ⟨L⟩
-  simpa only [Multiset.coe_prod, quot_mk_to_coe''] using roots_list_prod L
+theorem roots_multiset_prod (m : Multiset R[X]) : (0 : R[X]) ∉ m → m.Prod.roots = m.bind roots := by
+  rcases m with ⟨L⟩; simpa only [Multiset.coe_prod, quot_mk_to_coe''] using roots_list_prod L
 #align polynomial.roots_multiset_prod Polynomial.roots_multiset_prod
 -/
 
@@ -1085,9 +1072,7 @@ theorem roots_multiset_prod_X_sub_C (s : Multiset R) : (s.map fun a => X - C a).
   by
   rw [roots_multiset_prod, Multiset.bind_map]
   · simp_rw [roots_X_sub_C, Multiset.bind_singleton, Multiset.map_id']
-  · rw [Multiset.mem_map]
-    rintro ⟨a, -, h⟩
-    exact X_sub_C_ne_zero a h
+  · rw [Multiset.mem_map]; rintro ⟨a, -, h⟩; exact X_sub_C_ne_zero a h
 #align polynomial.roots_multiset_prod_X_sub_C Polynomial.roots_multiset_prod_X_sub_C
 
 /- warning: polynomial.nat_degree_multiset_prod_X_sub_C_eq_card -> Polynomial.natDegree_multiset_prod_X_sub_C_eq_card is a dubious translation:
@@ -1536,12 +1521,9 @@ theorem eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le {R} [CommRing R] {p
   obtain rfl | hq := eq_or_ne q 0; · simp
   have rzero : r ≠ 0 := fun h => by simpa [h, hq] using hr
   rw [hr, nat_degree_mul'] at hdeg; swap
-  · rw [hp.leading_coeff, one_mul, leading_coeff_ne_zero]
-    exact rzero
+  · rw [hp.leading_coeff, one_mul, leading_coeff_ne_zero]; exact rzero
   rw [mul_comm, @eq_C_of_nat_degree_eq_zero _ _ r] at hr
-  · convert hr
-    convert leading_coeff_C _ using 1
-    rw [hr, leading_coeff_mul_monic hp]
+  · convert hr; convert leading_coeff_C _ using 1; rw [hr, leading_coeff_mul_monic hp]
   · exact (add_right_inj _).1 (le_antisymm hdeg <| Nat.le.intro rfl)
 #align polynomial.eq_leading_coeff_mul_of_monic_of_dvd_of_nat_degree_le Polynomial.eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le
 
@@ -1562,8 +1544,7 @@ theorem isCoprime_X_sub_C_of_isUnit_sub {R} [CommRing R] {a b : R} (h : IsUnit (
   ⟨-C h.Unit⁻¹.val, C h.Unit⁻¹.val,
     by
     rw [neg_mul_comm, ← left_distrib, neg_add_eq_sub, sub_sub_sub_cancel_left, ← C_sub, ← C_mul]
-    convert C_1
-    exact h.coe_inv_mul⟩
+    convert C_1; exact h.coe_inv_mul⟩
 #align polynomial.is_coprime_X_sub_C_of_is_unit_sub Polynomial.isCoprime_X_sub_C_of_isUnit_sub
 
 /- warning: polynomial.pairwise_coprime_X_sub_C -> Polynomial.pairwise_coprime_X_sub_C is a dubious translation:
@@ -1634,9 +1615,7 @@ theorem exists_prod_multiset_X_sub_C_mul (p : R[X]) :
   obtain ⟨q, he⟩ := p.prod_multiset_X_sub_C_dvd
   use q, he.symm
   obtain rfl | hq := eq_or_ne q 0
-  · rw [MulZeroClass.mul_zero] at he
-    subst he
-    simp
+  · rw [MulZeroClass.mul_zero] at he; subst he; simp
   constructor
   · conv_rhs => rw [he]
     rw [monic_prod_multiset_X_sub_C.nat_degree_mul' hq, nat_degree_multiset_prod_X_sub_C_eq_card]
@@ -1663,10 +1642,8 @@ Case conversion may be inaccurate. Consider using '#align polynomial.prod_multis
 /-- A monic polynomial `p` that has as many roots as its degree
 can be written `p = ∏(X - a)`, for `a` in `p.roots`. -/
 theorem prod_multiset_X_sub_C_of_monic_of_roots_card_eq (hp : p.Monic)
-    (hroots : p.roots.card = p.natDegree) : (p.roots.map fun a => X - C a).Prod = p :=
-  by
-  convert C_leading_coeff_mul_prod_multiset_X_sub_C hroots
-  rw [hp.leading_coeff, C_1, one_mul]
+    (hroots : p.roots.card = p.natDegree) : (p.roots.map fun a => X - C a).Prod = p := by
+  convert C_leading_coeff_mul_prod_multiset_X_sub_C hroots; rw [hp.leading_coeff, C_1, one_mul]
 #align polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq Polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq
 
 end CommRing
@@ -1748,9 +1725,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align polynomial.map_roots_le Polynomial.map_roots_leₓ'. -/
 theorem map_roots_le [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (h : p.map f ≠ 0) :
     p.roots.map f ≤ (p.map f).roots :=
-  Multiset.le_iff_count.2 fun b => by
-    rw [count_roots]
-    apply count_map_roots h
+  Multiset.le_iff_count.2 fun b => by rw [count_roots]; apply count_map_roots h
 #align polynomial.map_roots_le Polynomial.map_roots_le
 
 /- warning: polynomial.map_roots_le_of_injective -> Polynomial.map_roots_le_of_injective is a dubious translation:
@@ -1770,9 +1745,7 @@ theorem map_roots_le_of_injective [IsDomain A] [IsDomain B] (p : A[X]) {f : A 
 <too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.card_roots_le_map Polynomial.card_roots_le_mapₓ'. -/
 theorem card_roots_le_map [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (h : p.map f ≠ 0) :
-    p.roots.card ≤ (p.map f).roots.card :=
-  by
-  rw [← p.roots.card_map f]
+    p.roots.card ≤ (p.map f).roots.card := by rw [← p.roots.card_map f];
   exact Multiset.card_le_of_le (map_roots_le h)
 #align polynomial.card_roots_le_map Polynomial.card_roots_le_map
 
@@ -1855,9 +1828,7 @@ theorem Monic.irreducible_of_irreducible_map (f : R[X]) (h_mon : Monic f)
         (h_irr.is_unit_or_is_unit <| (congr_arg (map φ) h).trans (Polynomial.map_mul φ)).imp _ _ <;>
       apply is_unit_of_is_unit_leading_coeff_of_is_unit_map <;>
     apply isUnit_of_mul_eq_one
-  · exact q;
-  · rw [mul_comm]
-    exact q
+  · exact q; · rw [mul_comm]; exact q
 #align polynomial.monic.irreducible_of_irreducible_map Polynomial.Monic.irreducible_of_irreducible_map
 
 end

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

@@ -512,10 +512,7 @@ section CommRing
 variable [CommRing R]
 
 /- warning: polynomial.le_root_multiplicity_iff -> Polynomial.le_rootMultiplicity_iff is a dubious translation:
-lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align polynomial.le_root_multiplicity_iff Polynomial.le_rootMultiplicity_iffₓ'. -/
 /-- The multiplicity of `a` as root of a nonzero polynomial `p` is at least `n` iff
   `(X - a) ^ n` divides `p`. -/
@@ -530,10 +527,7 @@ theorem le_rootMultiplicity_iff {p : R[X]} (p0 : p ≠ 0) {a : R} {n : ℕ} :
 #align polynomial.le_root_multiplicity_iff Polynomial.le_rootMultiplicity_iff
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.root_multiplicity_le_iff Polynomial.rootMultiplicity_le_iffₓ'. -/
 theorem rootMultiplicity_le_iff {p : R[X]} (p0 : p ≠ 0) (a : R) (n : ℕ) :
     rootMultiplicity a p ≤ n ↔ ¬(X - C a) ^ (n + 1) ∣ p := by
@@ -541,10 +535,7 @@ theorem rootMultiplicity_le_iff {p : R[X]} (p0 : p ≠ 0) (a : R) (n : ℕ) :
 #align polynomial.root_multiplicity_le_iff Polynomial.rootMultiplicity_le_iff
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.pow_root_multiplicity_not_dvd Polynomial.pow_rootMultiplicity_not_dvdₓ'. -/
 theorem pow_rootMultiplicity_not_dvd {p : R[X]} (p0 : p ≠ 0) (a : R) :
     ¬(X - C a) ^ (rootMultiplicity a p + 1) ∣ p := by rw [← root_multiplicity_le_iff p0]
@@ -702,10 +693,7 @@ theorem rootMultiplicity_X_sub_C_pow (a : R) (n : ℕ) : rootMultiplicity a ((X
 #align polynomial.root_multiplicity_X_sub_C_pow Polynomial.rootMultiplicity_X_sub_C_pow
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.exists_multiset_roots Polynomial.exists_multiset_rootsₓ'. -/
 theorem exists_multiset_roots :
     ∀ {p : R[X]} (hp : p ≠ 0),
@@ -791,10 +779,7 @@ theorem card_roots' (p : R[X]) : p.roots.card ≤ natDegree p :=
 #align polynomial.card_roots' Polynomial.card_roots'
 
 /- warning: polynomial.card_roots_sub_C -> Polynomial.card_roots_sub_C is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.card_roots_sub_C Polynomial.card_roots_sub_Cₓ'. -/
 theorem card_roots_sub_C {p : R[X]} {a : R} (hp0 : 0 < degree p) :
     ((p - C a).roots.card : WithBot ℕ) ≤ degree p :=
@@ -806,10 +791,7 @@ theorem card_roots_sub_C {p : R[X]} {a : R} (hp0 : 0 < degree p) :
 #align polynomial.card_roots_sub_C Polynomial.card_roots_sub_C
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.card_roots_sub_C' Polynomial.card_roots_sub_C'ₓ'. -/
 theorem card_roots_sub_C' {p : R[X]} {a : R} (hp0 : 0 < degree p) :
     (p - C a).roots.card ≤ natDegree p :=
@@ -922,10 +904,7 @@ theorem roots.le_of_dvd (h : q ≠ 0) : p ∣ q → roots p ≤ roots q :=
 #align polynomial.roots.le_of_dvd Polynomial.roots.le_of_dvd
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.mem_roots_sub_C' Polynomial.mem_roots_sub_C'ₓ'. -/
 theorem mem_roots_sub_C' {p : R[X]} {a x : R} : x ∈ (p - C a).roots ↔ p ≠ C a ∧ p.eval x = a := by
   rw [mem_roots', is_root.def, sub_ne_zero, eval_sub, sub_eq_zero, eval_C]
@@ -1070,20 +1049,14 @@ theorem roots_X_pow (n : ℕ) : (X ^ n : R[X]).roots = n • {0} := by rw [roots
 #align polynomial.roots_X_pow Polynomial.roots_X_pow
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_C_mul_X_pow Polynomial.roots_C_mul_X_powₓ'. -/
 theorem roots_C_mul_X_pow (ha : a ≠ 0) (n : ℕ) : (C a * X ^ n).roots = n • {0} := by
   rw [roots_C_mul _ ha, roots_X_pow]
 #align polynomial.roots_C_mul_X_pow Polynomial.roots_C_mul_X_pow
 
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 Case conversion may be inaccurate. Consider using '#align polynomial.roots_monomial Polynomial.roots_monomialₓ'. -/
 @[simp]
 theorem roots_monomial (ha : a ≠ 0) (n : ℕ) : (monomial n a).roots = n • {0} := by
@@ -1118,10 +1091,7 @@ theorem roots_multiset_prod_X_sub_C (s : Multiset R) : (s.map fun a => X - C a).
 #align polynomial.roots_multiset_prod_X_sub_C Polynomial.roots_multiset_prod_X_sub_C
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_multiset_prod_X_sub_C_eq_card Polynomial.natDegree_multiset_prod_X_sub_C_eq_cardₓ'. -/
 @[simp]
 theorem natDegree_multiset_prod_X_sub_C_eq_card (s : Multiset R) :
@@ -1135,10 +1105,7 @@ theorem natDegree_multiset_prod_X_sub_C_eq_card (s : Multiset R) :
 #align polynomial.nat_degree_multiset_prod_X_sub_C_eq_card Polynomial.natDegree_multiset_prod_X_sub_C_eq_card
 
 /- warning: polynomial.card_roots_X_pow_sub_C -> Polynomial.card_roots_X_pow_sub_C is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align polynomial.card_roots_X_pow_sub_C Polynomial.card_roots_X_pow_sub_Cₓ'. -/
 theorem card_roots_X_pow_sub_C {n : ℕ} (hn : 0 < n) (a : R) :
     (roots ((X : R[X]) ^ n - C a)).card ≤ n :=
@@ -1288,10 +1255,7 @@ theorem natDegree_coe_units (u : R[X]ˣ) : natDegree (u : R[X]) = 0 :=
 #align polynomial.nat_degree_coe_units Polynomial.natDegree_coe_units
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.comp_eq_zero_iff Polynomial.comp_eq_zero_iffₓ'. -/
 theorem comp_eq_zero_iff : p.comp q = 0 ↔ p = 0 ∨ p.eval (q.coeff 0) = 0 ∧ q = C (q.coeff 0) :=
   by
@@ -1357,10 +1321,7 @@ theorem rootSet_def (p : T[X]) (S) [CommRing S] [IsDomain S] [Algebra T S] :
 #align polynomial.root_set_def Polynomial.rootSet_def
 
 /- warning: polynomial.root_set_C -> Polynomial.rootSet_C is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align polynomial.root_set_C Polynomial.rootSet_Cₓ'. -/
 @[simp]
 theorem rootSet_C [CommRing S] [IsDomain S] [Algebra T S] (a : T) : (C a).rootSet S = ∅ := by
@@ -1421,10 +1382,7 @@ theorem bUnion_roots_finite {R S : Type _} [Semiring R] [CommRing S] [IsDomain S
 #align polynomial.bUnion_roots_finite Polynomial.bUnion_roots_finite
 
 /- warning: polynomial.mem_root_set' -> Polynomial.mem_rootSet' is a dubious translation:
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(CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (fun (_x : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (SMulZeroClass.toSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toZero.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (SMulZeroClass.toSMul.{u2, u1} T S (AddMonoid.toZero.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))))) (DistribSMul.toSMulZeroClass.{u2, u1} T S (AddMonoid.toAddZeroClass.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))))) (DistribMulAction.toDistribSMul.{u2, u1} T S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6 (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6))))) (Polynomial.aeval.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6 a) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.mem_root_set' Polynomial.mem_rootSet'ₓ'. -/
 theorem mem_rootSet' {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Algebra T S] {a : S} :
     a ∈ p.rootSet S ↔ p.map (algebraMap T S) ≠ 0 ∧ aeval a p = 0 := by
@@ -1433,10 +1391,7 @@ theorem mem_rootSet' {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Algebra
 #align polynomial.mem_root_set' Polynomial.mem_rootSet'
 
 /- warning: polynomial.mem_root_set -> Polynomial.mem_rootSet is a dubious translation:
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(CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T 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_inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T 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u1, max u1 u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6 (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6))))) (Polynomial.aeval.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6 a) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (IsDomain.toCancelCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) _inst_4) _inst_5)))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.mem_root_set Polynomial.mem_rootSetₓ'. -/
 theorem mem_rootSet {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Algebra T S]
     [NoZeroSMulDivisors T S] {a : S} : a ∈ p.rootSet S ↔ p ≠ 0 ∧ aeval a p = 0 := by
@@ -1445,10 +1400,7 @@ theorem mem_rootSet {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Algebra T
 #align polynomial.mem_root_set Polynomial.mem_rootSet
 
 /- warning: polynomial.mem_root_set_of_ne -> Polynomial.mem_rootSet_of_ne is a dubious translation:
-lean 3 declaration is
-  forall {T : Type.{u1}} [_inst_3 : CommRing.{u1} T] {p : Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))} {S : Type.{u2}} [_inst_4 : CommRing.{u2} S] [_inst_5 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_6 : Algebra.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_7 : NoZeroSMulDivisors.{u1, u2} T S (MulZeroClass.toHasZero.{u1} T (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} T (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} T (NonAssocRing.toNonUnitalNonAssocRing.{u1} T (Ring.toNonAssocRing.{u1} T (CommRing.toRing.{u1} T _inst_3)))))) (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_4)))))) (SMulZeroClass.toHasSmul.{u1, u2} T S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} T S (MulZeroClass.toHasZero.{u1} T (MulZeroOneClass.toMulZeroClass.{u1} T (MonoidWithZero.toMulZeroOneClass.{u1} T (Semiring.toMonoidWithZero.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} T S (Semiring.toMonoidWithZero.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) (Module.toMulActionWithZero.{u1, u2} T S (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))) (Algebra.toModule.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6)))))], (Ne.{succ u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) p (OfNat.ofNat.{u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) 0 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T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) (fun (_x : AlgHom.{u1, u1, u2} T (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) S (CommRing.toCommSemiring.{u1} T _inst_3) (Polynomial.semiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} T T (CommRing.toCommSemiring.{u1} T _inst_3) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Algebra.id.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) => (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) -> S) ([anonymous].{u1, u1, u2} T (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) S (CommRing.toCommSemiring.{u1} T _inst_3) (Polynomial.semiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} T T (CommRing.toCommSemiring.{u1} T _inst_3) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Algebra.id.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) (Polynomial.aeval.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6 a) p) (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_4)))))))))))
-but is expected to have type
-  forall {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] {p : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))} {S : Type.{u1}} [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))] [_inst_7 : NoZeroSMulDivisors.{u2, u1} T S (CommMonoidWithZero.toZero.{u2} T (CommSemiring.toCommMonoidWithZero.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommMonoidWithZero.toZero.{u1} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} S (IsDomain.toCancelCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4) _inst_5))) (Algebra.toSMul.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6)], (Ne.{succ u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) p (OfNat.ofNat.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.zero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) -> (forall {a : S}, Iff (Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) a (Polynomial.rootSet.{u2, u1} T _inst_3 p S _inst_4 _inst_5 _inst_6)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (fun (_x : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T 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T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (SMulZeroClass.toSMul.{u2, u1} T S (AddMonoid.toZero.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))))) (DistribSMul.toSMulZeroClass.{u2, u1} T S (AddMonoid.toAddZeroClass.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S 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(CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T 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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.mem_root_set_of_ne Polynomial.mem_rootSet_of_neₓ'. -/
 theorem mem_rootSet_of_ne {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Algebra T S]
     [NoZeroSMulDivisors T S] (hp : p ≠ 0) {a : S} : a ∈ p.rootSet S ↔ aeval a p = 0 :=
@@ -1456,10 +1408,7 @@ theorem mem_rootSet_of_ne {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Alg
 #align polynomial.mem_root_set_of_ne Polynomial.mem_rootSet_of_ne
 
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(CommRing.toCommSemiring.{u2} S _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)))) (Module.toDistribMulAction.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))) (Algebra.toModule.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) _inst_6)) (Module.toDistribMulAction.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' 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(CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9))))) f) (Polynomial.rootSet.{u3, u2} T _inst_3 p S _inst_4 _inst_5 _inst_6) (Polynomial.rootSet.{u3, u1} T _inst_3 p S' _inst_7 _inst_8 _inst_9))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.root_set_maps_to' Polynomial.rootSet_maps_to'ₓ'. -/
 theorem rootSet_maps_to' {p : T[X]} {S S'} [CommRing S] [IsDomain S] [Algebra T S] [CommRing S']
     [IsDomain S'] [Algebra T S'] (hp : p.map (algebraMap T S') = 0 → p.map (algebraMap T S) = 0)
@@ -1484,10 +1433,7 @@ theorem aeval_eq_zero_of_mem_rootSet {p : T[X]} [CommRing S] [IsDomain S] [Algeb
 -/
 
 /- warning: polynomial.root_set_maps_to -> Polynomial.rootSet_mapsTo is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.root_set_maps_to Polynomial.rootSet_mapsToₓ'. -/
 theorem rootSet_mapsTo {p : T[X]} {S S'} [CommRing S] [IsDomain S] [Algebra T S] [CommRing S']
     [IsDomain S'] [Algebra T S'] [NoZeroSMulDivisors T S'] (f : S →ₐ[T] S') :
@@ -1581,10 +1527,7 @@ theorem leadingCoeff_divByMonic_X_sub_C (p : R[X]) (hp : degree p ≠ 0) (a : R)
 #align polynomial.leading_coeff_div_by_monic_X_sub_C Polynomial.leadingCoeff_divByMonic_X_sub_C
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_leading_coeff_mul_of_monic_of_dvd_of_nat_degree_le Polynomial.eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_leₓ'. -/
 theorem eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le {R} [CommRing R] {p q : R[X]}
     (hp : p.Monic) (hdiv : p ∣ q) (hdeg : q.natDegree ≤ p.natDegree) : q = C q.leadingCoeff * p :=
@@ -1612,10 +1555,7 @@ theorem eq_of_monic_of_dvd_of_natDegree_le {R} [CommRing R] {p q : R[X]} (hp : p
 -/
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.is_coprime_X_sub_C_of_is_unit_sub Polynomial.isCoprime_X_sub_C_of_isUnit_subₓ'. -/
 theorem isCoprime_X_sub_C_of_isUnit_sub {R} [CommRing R] {a b : R} (h : IsUnit (a - b)) :
     IsCoprime (X - C a) (X - C b) :=
@@ -1627,10 +1567,7 @@ theorem isCoprime_X_sub_C_of_isUnit_sub {R} [CommRing R] {a b : R} (h : IsUnit (
 #align polynomial.is_coprime_X_sub_C_of_is_unit_sub Polynomial.isCoprime_X_sub_C_of_isUnit_sub
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.pairwise_coprime_X_sub_C Polynomial.pairwise_coprime_X_sub_Cₓ'. -/
 theorem pairwise_coprime_X_sub_C {K} [Field K] {I : Type v} {s : I → K} (H : Function.Injective s) :
     Pairwise (IsCoprime on fun i : I => X - C (s i)) := fun i j hij =>
@@ -1648,10 +1585,7 @@ theorem monic_prod_multiset_X_sub_C : Monic (p.roots.map fun a => X - C a).Prod
 #align polynomial.monic_prod_multiset_X_sub_C Polynomial.monic_prod_multiset_X_sub_C
 
 /- warning: polynomial.prod_multiset_root_eq_finset_root -> Polynomial.prod_multiset_root_eq_finset_root is a dubious translation:
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(Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (Polynomial.rootMultiplicity.{u1} R _inst_1 a 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))] {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))) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.prod_multiset_root_eq_finset_root Polynomial.prod_multiset_root_eq_finset_rootₓ'. -/
 theorem prod_multiset_root_eq_finset_root :
     (p.roots.map fun a => X - C a).Prod =
@@ -1660,10 +1594,7 @@ theorem prod_multiset_root_eq_finset_root :
 #align polynomial.prod_multiset_root_eq_finset_root Polynomial.prod_multiset_root_eq_finset_root
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.prod_multiset_X_sub_C_dvd Polynomial.prod_multiset_X_sub_C_dvdₓ'. -/
 /-- The product `∏ (X - a)` for `a` inside the multiset `p.roots` divides `p`. -/
 theorem prod_multiset_X_sub_C_dvd (p : R[X]) : (p.roots.map fun a => X - C a).Prod ∣ p :=
@@ -1677,10 +1608,7 @@ theorem prod_multiset_X_sub_C_dvd (p : R[X]) : (p.roots.map fun a => X - C a).Pr
 #align polynomial.prod_multiset_X_sub_C_dvd Polynomial.prod_multiset_X_sub_C_dvd
 
 /- warning: multiset.prod_X_sub_C_dvd_iff_le_roots -> Multiset.prod_X_sub_C_dvd_iff_le_roots is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align multiset.prod_X_sub_C_dvd_iff_le_roots Multiset.prod_X_sub_C_dvd_iff_le_rootsₓ'. -/
 /-- A Galois connection. -/
 theorem Multiset.prod_X_sub_C_dvd_iff_le_roots {p : R[X]} (hp : p ≠ 0) (s : Multiset R) :
@@ -1696,10 +1624,7 @@ theorem Multiset.prod_X_sub_C_dvd_iff_le_roots {p : R[X]} (hp : p ≠ 0) (s : Mu
 #align multiset.prod_X_sub_C_dvd_iff_le_roots Multiset.prod_X_sub_C_dvd_iff_le_roots
 
 /- warning: polynomial.exists_prod_multiset_X_sub_C_mul -> Polynomial.exists_prod_multiset_X_sub_C_mul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.exists_prod_multiset_X_sub_C_mul Polynomial.exists_prod_multiset_X_sub_C_mulₓ'. -/
 theorem exists_prod_multiset_X_sub_C_mul (p : R[X]) :
     ∃ q,
@@ -1721,10 +1646,7 @@ theorem exists_prod_multiset_X_sub_C_mul (p : R[X]) :
 #align polynomial.exists_prod_multiset_X_sub_C_mul Polynomial.exists_prod_multiset_X_sub_C_mul
 
 /- warning: polynomial.C_leading_coeff_mul_prod_multiset_X_sub_C -> Polynomial.C_leadingCoeff_mul_prod_multiset_X_sub_C is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.C_leading_coeff_mul_prod_multiset_X_sub_C Polynomial.C_leadingCoeff_mul_prod_multiset_X_sub_Cₓ'. -/
 /-- A polynomial `p` that has as many roots as its degree
 can be written `p = p.leading_coeff * ∏(X - a)`, for `a` in `p.roots`. -/
@@ -1736,10 +1658,7 @@ theorem C_leadingCoeff_mul_prod_multiset_X_sub_C (hroots : p.roots.card = p.natD
 #align polynomial.C_leading_coeff_mul_prod_multiset_X_sub_C Polynomial.C_leadingCoeff_mul_prod_multiset_X_sub_C
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq Polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eqₓ'. -/
 /-- A monic polynomial `p` that has as many roots as its degree
 can be written `p = ∏(X - a)`, for `a` in `p.roots`. -/
@@ -1848,10 +1767,7 @@ theorem map_roots_le_of_injective [IsDomain A] [IsDomain B] (p : A[X]) {f : A 
 #align polynomial.map_roots_le_of_injective Polynomial.map_roots_le_of_injective
 
 /- warning: polynomial.card_roots_le_map -> Polynomial.card_roots_le_map is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.card_roots_le_map Polynomial.card_roots_le_mapₓ'. -/
 theorem card_roots_le_map [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (h : p.map f ≠ 0) :
     p.roots.card ≤ (p.map f).roots.card :=
@@ -1861,10 +1777,7 @@ theorem card_roots_le_map [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (
 #align polynomial.card_roots_le_map Polynomial.card_roots_le_map
 
 /- warning: polynomial.card_roots_le_map_of_injective -> Polynomial.card_roots_le_map_of_injective is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.card_roots_le_map_of_injective Polynomial.card_roots_le_map_of_injectiveₓ'. -/
 theorem card_roots_le_map_of_injective [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B}
     (hf : Function.Injective f) : p.roots.card ≤ (p.map f).roots.card :=
@@ -1874,10 +1787,7 @@ theorem card_roots_le_map_of_injective [IsDomain A] [IsDomain B] {p : A[X]} {f :
 #align polynomial.card_roots_le_map_of_injective Polynomial.card_roots_le_map_of_injective
 
 /- warning: polynomial.roots_map_of_injective_of_card_eq_nat_degree -> Polynomial.roots_map_of_injective_of_card_eq_natDegree is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align polynomial.roots_map_of_injective_of_card_eq_nat_degree Polynomial.roots_map_of_injective_of_card_eq_natDegreeₓ'. -/
 theorem roots_map_of_injective_of_card_eq_natDegree [IsDomain A] [IsDomain B] {p : A[X]}
     {f : A →+* B} (hf : Function.Injective f) (hroots : p.roots.card = p.natDegree) :

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

@@ -1083,7 +1083,7 @@ theorem roots_C_mul_X_pow (ha : a ≠ 0) (n : ℕ) : (C a * X ^ n).roots = n •
 lean 3 declaration is
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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)))))) (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)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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)))))) (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))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (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} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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)))))) (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.monomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) n) a)) (SMul.smul.{0, u1} Nat (Multiset.{u1} R) (AddMonoid.SMul.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) n (Singleton.singleton.{u1, u1} R (Multiset.{u1} R) (Multiset.hasSingleton.{u1} R) (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 (CommRing.toRing.{u1} R _inst_1))))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))], (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))) -> (forall (n : Nat), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (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)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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)))))) (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))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (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} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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)))))) (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.monomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) n) a)) (HSMul.hSMul.{0, u1, u1} Nat (Multiset.{u1} R) (Multiset.{u1} R) (instHSMul.{0, u1} Nat (Multiset.{u1} R) (AddMonoid.SMul.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) n (Singleton.singleton.{u1, u1} R (Multiset.{u1} R) (Multiset.instSingletonMultiset.{u1} R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))))))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))], (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))) -> (forall (n : Nat), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (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)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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)))))) (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))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (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} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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)))))) (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.monomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) n) a)) (HSMul.hSMul.{0, u1, u1} Nat (Multiset.{u1} R) (Multiset.{u1} R) (instHSMul.{0, u1} Nat (Multiset.{u1} R) (AddMonoid.SMul.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) n (Singleton.singleton.{u1, u1} R (Multiset.{u1} R) (Multiset.instSingletonMultiset.{u1} R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_monomial Polynomial.roots_monomialₓ'. -/
 @[simp]
 theorem roots_monomial (ha : a ≠ 0) (n : ℕ) : (monomial n a).roots = n • {0} := by
@@ -1424,7 +1424,7 @@ theorem bUnion_roots_finite {R S : Type _} [Semiring R] [CommRing S] [IsDomain S
 lean 3 declaration is
   forall {T : Type.{u1}} [_inst_3 : CommRing.{u1} T] {p : Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))} {S : Type.{u2}} [_inst_4 : CommRing.{u2} S] [_inst_5 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_6 : Algebra.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] {a : S}, Iff (Membership.Mem.{u2, u2} S (Set.{u2} S) (Set.hasMem.{u2} S) a (Polynomial.rootSet.{u1, u2} T _inst_3 p S _inst_4 _inst_5 _inst_6)) (And (Ne.{succ u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))) (Polynomial.map.{u1, u2} T S (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (algebraMap.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6) p) (OfNat.ofNat.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))) 0 (OfNat.mk.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))) 0 (Zero.zero.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))) (Polynomial.zero.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))))) (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} T (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) S (CommRing.toCommSemiring.{u1} T _inst_3) (Polynomial.semiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} T T (CommRing.toCommSemiring.{u1} T _inst_3) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Algebra.id.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) (fun (_x : AlgHom.{u1, u1, u2} T (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) S (CommRing.toCommSemiring.{u1} T _inst_3) (Polynomial.semiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} T T (CommRing.toCommSemiring.{u1} T _inst_3) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Algebra.id.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) => (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) -> S) ([anonymous].{u1, u1, u2} T (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) S (CommRing.toCommSemiring.{u1} T _inst_3) (Polynomial.semiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} T T (CommRing.toCommSemiring.{u1} T _inst_3) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Algebra.id.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) (Polynomial.aeval.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6 a) p) (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_4)))))))))))
 but is expected to have type
-  forall {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] {p : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))} {S : Type.{u1}} [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))] {a : S}, Iff (Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) a (Polynomial.rootSet.{u2, u1} T _inst_3 p S _inst_4 _inst_5 _inst_6)) (And (Ne.{succ u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))) (Polynomial.map.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (algebraMap.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6) p) (OfNat.ofNat.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))) (Polynomial.zero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))))) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (fun (_x : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (SMulZeroClass.toSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toZero.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (SMulZeroClass.toSMul.{u2, u1} T S (AddMonoid.toZero.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))))) (DistribSMul.toSMulZeroClass.{u2, u1} T S (AddMonoid.toAddZeroClass.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))))) (DistribMulAction.toDistribSMul.{u2, u1} T S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6 (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6))))) (Polynomial.aeval.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6 a) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (IsDomain.toCancelCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) _inst_4) _inst_5)))))))
+  forall {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] {p : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))} {S : Type.{u1}} [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))] {a : S}, Iff (Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) a (Polynomial.rootSet.{u2, u1} T _inst_3 p S _inst_4 _inst_5 _inst_6)) (And (Ne.{succ u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))) (Polynomial.map.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (algebraMap.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6) p) (OfNat.ofNat.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))) (Polynomial.zero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))))) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (fun (_x : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (SMulZeroClass.toSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toZero.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (SMulZeroClass.toSMul.{u2, u1} T S (AddMonoid.toZero.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))))) (DistribSMul.toSMulZeroClass.{u2, u1} T S (AddMonoid.toAddZeroClass.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))))) (DistribMulAction.toDistribSMul.{u2, u1} T S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6 (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6))))) (Polynomial.aeval.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6 a) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (IsDomain.toCancelCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) _inst_4) _inst_5)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.mem_root_set' Polynomial.mem_rootSet'ₓ'. -/
 theorem mem_rootSet' {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Algebra T S] {a : S} :
     a ∈ p.rootSet S ↔ p.map (algebraMap T S) ≠ 0 ∧ aeval a p = 0 := by
@@ -1436,7 +1436,7 @@ theorem mem_rootSet' {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Algebra
 lean 3 declaration is
   forall {T : Type.{u1}} [_inst_3 : CommRing.{u1} T] {p : Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))} {S : Type.{u2}} [_inst_4 : CommRing.{u2} S] [_inst_5 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_6 : Algebra.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_7 : NoZeroSMulDivisors.{u1, u2} T S (MulZeroClass.toHasZero.{u1} T (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} T (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} T (NonAssocRing.toNonUnitalNonAssocRing.{u1} T (Ring.toNonAssocRing.{u1} T (CommRing.toRing.{u1} T _inst_3)))))) (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_4)))))) (SMulZeroClass.toHasSmul.{u1, u2} T S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} T S (MulZeroClass.toHasZero.{u1} T (MulZeroOneClass.toMulZeroClass.{u1} T (MonoidWithZero.toMulZeroOneClass.{u1} T (Semiring.toMonoidWithZero.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} T S (Semiring.toMonoidWithZero.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) (Module.toMulActionWithZero.{u1, u2} T S (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))) (Algebra.toModule.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6)))))] {a : S}, Iff (Membership.Mem.{u2, u2} S (Set.{u2} S) (Set.hasMem.{u2} S) a (Polynomial.rootSet.{u1, u2} T _inst_3 p S _inst_4 _inst_5 _inst_6)) (And (Ne.{succ u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) p (OfNat.ofNat.{u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) 0 (OfNat.mk.{u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) 0 (Zero.zero.{u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) (Polynomial.zero.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))))))) (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} T (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) S (CommRing.toCommSemiring.{u1} T _inst_3) (Polynomial.semiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} T T (CommRing.toCommSemiring.{u1} T _inst_3) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Algebra.id.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) (fun (_x : AlgHom.{u1, u1, u2} T (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) S (CommRing.toCommSemiring.{u1} T _inst_3) (Polynomial.semiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} T T (CommRing.toCommSemiring.{u1} T _inst_3) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Algebra.id.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) => (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) -> S) ([anonymous].{u1, u1, u2} T (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) S (CommRing.toCommSemiring.{u1} T _inst_3) (Polynomial.semiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} T T (CommRing.toCommSemiring.{u1} T _inst_3) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Algebra.id.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) (Polynomial.aeval.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6 a) p) (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_4)))))))))))
 but is expected to have type
-  forall {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] {p : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))} {S : Type.{u1}} [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))] [_inst_7 : NoZeroSMulDivisors.{u2, u1} T S (CommMonoidWithZero.toZero.{u2} T (CommSemiring.toCommMonoidWithZero.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommMonoidWithZero.toZero.{u1} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} S (IsDomain.toCancelCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4) _inst_5))) (Algebra.toSMul.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6)] {a : S}, Iff (Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) a (Polynomial.rootSet.{u2, u1} T _inst_3 p S _inst_4 _inst_5 _inst_6)) (And (Ne.{succ u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) p (OfNat.ofNat.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.zero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (fun (_x : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (SMulZeroClass.toSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toZero.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (SMulZeroClass.toSMul.{u2, u1} T S (AddMonoid.toZero.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))))) (DistribSMul.toSMulZeroClass.{u2, u1} T S (AddMonoid.toAddZeroClass.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))))) (DistribMulAction.toDistribSMul.{u2, u1} T S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6 (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6))))) (Polynomial.aeval.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6 a) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (IsDomain.toCancelCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) _inst_4) _inst_5)))))))
+  forall {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] {p : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))} {S : Type.{u1}} [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))] [_inst_7 : NoZeroSMulDivisors.{u2, u1} T S (CommMonoidWithZero.toZero.{u2} T (CommSemiring.toCommMonoidWithZero.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommMonoidWithZero.toZero.{u1} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} S (IsDomain.toCancelCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4) _inst_5))) (Algebra.toSMul.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6)] {a : S}, Iff (Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) a (Polynomial.rootSet.{u2, u1} T _inst_3 p S _inst_4 _inst_5 _inst_6)) (And (Ne.{succ u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) p (OfNat.ofNat.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.zero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (fun (_x : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (SMulZeroClass.toSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toZero.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (SMulZeroClass.toSMul.{u2, u1} T S (AddMonoid.toZero.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))))) (DistribSMul.toSMulZeroClass.{u2, u1} T S (AddMonoid.toAddZeroClass.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))))) (DistribMulAction.toDistribSMul.{u2, u1} T S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6 (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6))))) (Polynomial.aeval.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6 a) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (IsDomain.toCancelCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) _inst_4) _inst_5)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.mem_root_set Polynomial.mem_rootSetₓ'. -/
 theorem mem_rootSet {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Algebra T S]
     [NoZeroSMulDivisors T S] {a : S} : a ∈ p.rootSet S ↔ p ≠ 0 ∧ aeval a p = 0 := by
@@ -1448,7 +1448,7 @@ theorem mem_rootSet {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Algebra T
 lean 3 declaration is
   forall {T : Type.{u1}} [_inst_3 : CommRing.{u1} T] {p : Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))} {S : Type.{u2}} [_inst_4 : CommRing.{u2} S] [_inst_5 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_6 : Algebra.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_7 : NoZeroSMulDivisors.{u1, u2} T S (MulZeroClass.toHasZero.{u1} T (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} T (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} T (NonAssocRing.toNonUnitalNonAssocRing.{u1} T (Ring.toNonAssocRing.{u1} T (CommRing.toRing.{u1} T _inst_3)))))) (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_4)))))) (SMulZeroClass.toHasSmul.{u1, u2} T S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} T S (MulZeroClass.toHasZero.{u1} T (MulZeroOneClass.toMulZeroClass.{u1} T (MonoidWithZero.toMulZeroOneClass.{u1} T (Semiring.toMonoidWithZero.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} T S (Semiring.toMonoidWithZero.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) (Module.toMulActionWithZero.{u1, u2} T S (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))) (Algebra.toModule.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6)))))], (Ne.{succ u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) p (OfNat.ofNat.{u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) 0 (OfNat.mk.{u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) 0 (Zero.zero.{u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) (Polynomial.zero.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))))))) -> (forall {a : S}, Iff (Membership.Mem.{u2, u2} S (Set.{u2} S) (Set.hasMem.{u2} S) a (Polynomial.rootSet.{u1, u2} T _inst_3 p S _inst_4 _inst_5 _inst_6)) (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} T (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) S (CommRing.toCommSemiring.{u1} T _inst_3) (Polynomial.semiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} T T (CommRing.toCommSemiring.{u1} T _inst_3) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Algebra.id.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) (fun (_x : AlgHom.{u1, u1, u2} T (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) S (CommRing.toCommSemiring.{u1} T _inst_3) (Polynomial.semiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} T T (CommRing.toCommSemiring.{u1} T _inst_3) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Algebra.id.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) => (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) -> S) ([anonymous].{u1, u1, u2} T (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) S (CommRing.toCommSemiring.{u1} T _inst_3) (Polynomial.semiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} T T (CommRing.toCommSemiring.{u1} T _inst_3) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Algebra.id.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) (Polynomial.aeval.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6 a) p) (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_4)))))))))))
 but is expected to have type
-  forall {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] {p : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))} {S : Type.{u1}} [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))] [_inst_7 : NoZeroSMulDivisors.{u2, u1} T S (CommMonoidWithZero.toZero.{u2} T (CommSemiring.toCommMonoidWithZero.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommMonoidWithZero.toZero.{u1} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} S (IsDomain.toCancelCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4) _inst_5))) (Algebra.toSMul.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6)], (Ne.{succ u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) p (OfNat.ofNat.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.zero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) -> (forall {a : S}, Iff (Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) a (Polynomial.rootSet.{u2, u1} T _inst_3 p S _inst_4 _inst_5 _inst_6)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (fun (_x : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (SMulZeroClass.toSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toZero.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (SMulZeroClass.toSMul.{u2, u1} T S (AddMonoid.toZero.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))))) (DistribSMul.toSMulZeroClass.{u2, u1} T S (AddMonoid.toAddZeroClass.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))))) (DistribMulAction.toDistribSMul.{u2, u1} T S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6 (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6))))) (Polynomial.aeval.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6 a) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (IsDomain.toCancelCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) _inst_4) _inst_5)))))))
+  forall {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] {p : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))} {S : Type.{u1}} [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))] [_inst_7 : NoZeroSMulDivisors.{u2, u1} T S (CommMonoidWithZero.toZero.{u2} T (CommSemiring.toCommMonoidWithZero.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommMonoidWithZero.toZero.{u1} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} S (IsDomain.toCancelCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4) _inst_5))) (Algebra.toSMul.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6)], (Ne.{succ u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) p (OfNat.ofNat.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.zero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) -> (forall {a : S}, Iff (Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) a (Polynomial.rootSet.{u2, u1} T _inst_3 p S _inst_4 _inst_5 _inst_6)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (fun (_x : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (SMulZeroClass.toSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toZero.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (SMulZeroClass.toSMul.{u2, u1} T S (AddMonoid.toZero.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))))) (DistribSMul.toSMulZeroClass.{u2, u1} T S (AddMonoid.toAddZeroClass.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))))) (DistribMulAction.toDistribSMul.{u2, u1} T S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6 (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6))))) (Polynomial.aeval.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6 a) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (IsDomain.toCancelCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) _inst_4) _inst_5)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.mem_root_set_of_ne Polynomial.mem_rootSet_of_neₓ'. -/
 theorem mem_rootSet_of_ne {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Algebra T S]
     [NoZeroSMulDivisors T S] (hp : p ≠ 0) {a : S} : a ∈ p.rootSet S ↔ aeval a p = 0 :=
@@ -1459,7 +1459,7 @@ theorem mem_rootSet_of_ne {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Alg
 lean 3 declaration is
   forall {T : Type.{u1}} [_inst_3 : CommRing.{u1} T] {p : Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))} {S : Type.{u2}} {S' : Type.{u3}} [_inst_4 : CommRing.{u2} S] [_inst_5 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_6 : Algebra.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_7 : CommRing.{u3} S'] [_inst_8 : IsDomain.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7))] [_inst_9 : Algebra.{u1, u3} T S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7))], ((Eq.{succ u3} (Polynomial.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7))) (Polynomial.map.{u1, u3} T S' (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)) (algebraMap.{u1, u3} T S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)) _inst_9) p) (OfNat.ofNat.{u3} (Polynomial.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7))) 0 (OfNat.mk.{u3} (Polynomial.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7))) 0 (Zero.zero.{u3} (Polynomial.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7))) (Polynomial.zero.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7))))))) -> (Eq.{succ u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))) (Polynomial.map.{u1, u2} T S (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (algebraMap.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6) p) (OfNat.ofNat.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))) 0 (OfNat.mk.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))) 0 (Zero.zero.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))) (Polynomial.zero.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) -> (forall (f : AlgHom.{u1, u2, u3} T S S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)) _inst_6 _inst_9), Set.MapsTo.{u2, u3} S S' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} T S S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)) _inst_6 _inst_9) (fun (_x : AlgHom.{u1, u2, u3} T S S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)) _inst_6 _inst_9) => S -> S') ([anonymous].{u1, u2, u3} T S S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)) _inst_6 _inst_9) f) (Polynomial.rootSet.{u1, u2} T _inst_3 p S _inst_4 _inst_5 _inst_6) (Polynomial.rootSet.{u1, u3} T _inst_3 p S' _inst_7 _inst_8 _inst_9))
 but is expected to have type
-  forall {T : Type.{u3}} [_inst_3 : CommRing.{u3} T] {p : Polynomial.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3))} {S : Type.{u2}} {S' : Type.{u1}} [_inst_4 : CommRing.{u2} S] [_inst_5 : IsDomain.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))] [_inst_6 : Algebra.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))] [_inst_7 : CommRing.{u1} S'] [_inst_8 : IsDomain.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))] [_inst_9 : Algebra.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))], ((Eq.{succ u1} (Polynomial.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))) (Polynomial.map.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) (algebraMap.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_9) p) (OfNat.ofNat.{u1} (Polynomial.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))) (Polynomial.zero.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)))))) -> (Eq.{succ u2} (Polynomial.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))) (Polynomial.map.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (algebraMap.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) _inst_6) p) (OfNat.ofNat.{u2} (Polynomial.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))) (Polynomial.zero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))))) -> (forall (f : AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9), Set.MapsTo.{u2, u1} S S' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) T S S' (SMulZeroClass.toSMul.{u3, u2} T S (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))))) (DistribSMul.toSMulZeroClass.{u3, u2} T S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))))) (DistribMulAction.toDistribSMul.{u3, u2} T S (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))))) (Module.toDistribMulAction.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))) (Algebra.toModule.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) _inst_6))))) (SMulZeroClass.toSMul.{u3, u1} T S' (AddMonoid.toZero.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))))) (DistribSMul.toSMulZeroClass.{u3, u1} T S' (AddMonoid.toAddZeroClass.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))))) (DistribMulAction.toDistribSMul.{u3, u1} T S' (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)))))) (Module.toDistribMulAction.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))) (Algebra.toModule.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) T S S' (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)))))) (Module.toDistribMulAction.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))) (Algebra.toModule.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) _inst_6)) (Module.toDistribMulAction.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))) (Algebra.toModule.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_9)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) T S S' (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)))) (Module.toDistribMulAction.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))) (Algebra.toModule.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) _inst_6)) (Module.toDistribMulAction.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))) (Algebra.toModule.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_9)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9 (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) (AlgHom.algHomClass.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9))))) f) (Polynomial.rootSet.{u3, u2} T _inst_3 p S _inst_4 _inst_5 _inst_6) (Polynomial.rootSet.{u3, u1} T _inst_3 p S' _inst_7 _inst_8 _inst_9))
+  forall {T : Type.{u3}} [_inst_3 : CommRing.{u3} T] {p : Polynomial.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3))} {S : Type.{u2}} {S' : Type.{u1}} [_inst_4 : CommRing.{u2} S] [_inst_5 : IsDomain.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))] [_inst_6 : Algebra.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))] [_inst_7 : CommRing.{u1} S'] [_inst_8 : IsDomain.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))] [_inst_9 : Algebra.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))], ((Eq.{succ u1} (Polynomial.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))) (Polynomial.map.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) (algebraMap.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_9) p) (OfNat.ofNat.{u1} (Polynomial.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))) (Polynomial.zero.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)))))) -> (Eq.{succ u2} (Polynomial.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))) (Polynomial.map.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (algebraMap.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) _inst_6) p) (OfNat.ofNat.{u2} (Polynomial.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))) (Polynomial.zero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))))) -> (forall (f : AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9), Set.MapsTo.{u2, u1} S S' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : S) => S') _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) T S S' (SMulZeroClass.toSMul.{u3, u2} T S (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))))) (DistribSMul.toSMulZeroClass.{u3, u2} T S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))))) (DistribMulAction.toDistribSMul.{u3, u2} T S (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))))) (Module.toDistribMulAction.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))) (Algebra.toModule.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) _inst_6))))) (SMulZeroClass.toSMul.{u3, u1} T S' (AddMonoid.toZero.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))))) (DistribSMul.toSMulZeroClass.{u3, u1} T S' (AddMonoid.toAddZeroClass.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))))) (DistribMulAction.toDistribSMul.{u3, u1} T S' (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)))))) (Module.toDistribMulAction.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))) (Algebra.toModule.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) T S S' (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)))))) (Module.toDistribMulAction.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))) (Algebra.toModule.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) _inst_6)) (Module.toDistribMulAction.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))) (Algebra.toModule.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_9)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) T S S' (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)))) (Module.toDistribMulAction.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))) (Algebra.toModule.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) _inst_6)) (Module.toDistribMulAction.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))) (Algebra.toModule.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_9)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9 (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) (AlgHom.algHomClass.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9))))) f) (Polynomial.rootSet.{u3, u2} T _inst_3 p S _inst_4 _inst_5 _inst_6) (Polynomial.rootSet.{u3, u1} T _inst_3 p S' _inst_7 _inst_8 _inst_9))
 Case conversion may be inaccurate. Consider using '#align polynomial.root_set_maps_to' Polynomial.rootSet_maps_to'ₓ'. -/
 theorem rootSet_maps_to' {p : T[X]} {S S'} [CommRing S] [IsDomain S] [Algebra T S] [CommRing S']
     [IsDomain S'] [Algebra T S'] (hp : p.map (algebraMap T S') = 0 → p.map (algebraMap T S) = 0)
@@ -1487,7 +1487,7 @@ theorem aeval_eq_zero_of_mem_rootSet {p : T[X]} [CommRing S] [IsDomain S] [Algeb
 lean 3 declaration is
   forall {T : Type.{u1}} [_inst_3 : CommRing.{u1} T] {p : Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))} {S : Type.{u2}} {S' : Type.{u3}} [_inst_4 : CommRing.{u2} S] [_inst_5 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_6 : Algebra.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_7 : CommRing.{u3} S'] [_inst_8 : IsDomain.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7))] [_inst_9 : Algebra.{u1, u3} T S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7))] [_inst_10 : NoZeroSMulDivisors.{u1, u3} T S' (MulZeroClass.toHasZero.{u1} T (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} T (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} T (NonAssocRing.toNonUnitalNonAssocRing.{u1} T (Ring.toNonAssocRing.{u1} T (CommRing.toRing.{u1} T _inst_3)))))) (MulZeroClass.toHasZero.{u3} S' (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} S' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} S' (NonAssocRing.toNonUnitalNonAssocRing.{u3} S' (Ring.toNonAssocRing.{u3} S' (CommRing.toRing.{u3} S' _inst_7)))))) (SMulZeroClass.toHasSmul.{u1, u3} T S' (AddZeroClass.toHasZero.{u3} S' (AddMonoid.toAddZeroClass.{u3} S' (AddCommMonoid.toAddMonoid.{u3} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S' (Semiring.toNonAssocSemiring.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} T S' (MulZeroClass.toHasZero.{u1} T (MulZeroOneClass.toMulZeroClass.{u1} T (MonoidWithZero.toMulZeroOneClass.{u1} T (Semiring.toMonoidWithZero.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)))))) (AddZeroClass.toHasZero.{u3} S' (AddMonoid.toAddZeroClass.{u3} S' (AddCommMonoid.toAddMonoid.{u3} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S' (Semiring.toNonAssocSemiring.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} T S' (Semiring.toMonoidWithZero.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (AddZeroClass.toHasZero.{u3} S' (AddMonoid.toAddZeroClass.{u3} S' (AddCommMonoid.toAddMonoid.{u3} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S' (Semiring.toNonAssocSemiring.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)))))))) (Module.toMulActionWithZero.{u1, u3} T S' (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S' (Semiring.toNonAssocSemiring.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7))))) (Algebra.toModule.{u1, u3} T S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)) _inst_9)))))] (f : AlgHom.{u1, u2, u3} T S S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)) _inst_6 _inst_9), Set.MapsTo.{u2, u3} S S' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} T S S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)) _inst_6 _inst_9) (fun (_x : AlgHom.{u1, u2, u3} T S S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)) _inst_6 _inst_9) => S -> S') ([anonymous].{u1, u2, u3} T S S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)) _inst_6 _inst_9) f) (Polynomial.rootSet.{u1, u2} T _inst_3 p S _inst_4 _inst_5 _inst_6) (Polynomial.rootSet.{u1, u3} T _inst_3 p S' _inst_7 _inst_8 _inst_9)
 but is expected to have type
-  forall {T : Type.{u3}} [_inst_3 : CommRing.{u3} T] {p : Polynomial.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3))} {S : Type.{u2}} {S' : Type.{u1}} [_inst_4 : CommRing.{u2} S] [_inst_5 : IsDomain.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))] [_inst_6 : Algebra.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))] [_inst_7 : CommRing.{u1} S'] [_inst_8 : IsDomain.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))] [_inst_9 : Algebra.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))] [_inst_10 : NoZeroSMulDivisors.{u3, u1} T S' (CommMonoidWithZero.toZero.{u3} T (CommSemiring.toCommMonoidWithZero.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3))) (CommMonoidWithZero.toZero.{u1} S' (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} S' (IsDomain.toCancelCommMonoidWithZero.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_9)] (f : AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9), Set.MapsTo.{u2, u1} S S' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) T S S' (SMulZeroClass.toSMul.{u3, u2} T S (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))))) (DistribSMul.toSMulZeroClass.{u3, u2} T S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))))) (DistribMulAction.toDistribSMul.{u3, u2} T S (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))))) (Module.toDistribMulAction.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))) (Algebra.toModule.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) _inst_6))))) (SMulZeroClass.toSMul.{u3, u1} T S' (AddMonoid.toZero.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))))) (DistribSMul.toSMulZeroClass.{u3, u1} T S' (AddMonoid.toAddZeroClass.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))))) (DistribMulAction.toDistribSMul.{u3, u1} T S' (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)))))) (Module.toDistribMulAction.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))) (Algebra.toModule.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) T S S' (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)))))) (Module.toDistribMulAction.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))) (Algebra.toModule.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) _inst_6)) (Module.toDistribMulAction.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))) (Algebra.toModule.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_9)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) T S S' (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)))) (Module.toDistribMulAction.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))) (Algebra.toModule.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) _inst_6)) (Module.toDistribMulAction.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))) (Algebra.toModule.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_9)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9 (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) (AlgHom.algHomClass.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9))))) f) (Polynomial.rootSet.{u3, u2} T _inst_3 p S _inst_4 _inst_5 _inst_6) (Polynomial.rootSet.{u3, u1} T _inst_3 p S' _inst_7 _inst_8 _inst_9)
+  forall {T : Type.{u3}} [_inst_3 : CommRing.{u3} T] {p : Polynomial.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3))} {S : Type.{u2}} {S' : Type.{u1}} [_inst_4 : CommRing.{u2} S] [_inst_5 : IsDomain.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))] [_inst_6 : Algebra.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))] [_inst_7 : CommRing.{u1} S'] [_inst_8 : IsDomain.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))] [_inst_9 : Algebra.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))] [_inst_10 : NoZeroSMulDivisors.{u3, u1} T S' (CommMonoidWithZero.toZero.{u3} T (CommSemiring.toCommMonoidWithZero.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3))) (CommMonoidWithZero.toZero.{u1} S' (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} S' (IsDomain.toCancelCommMonoidWithZero.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_9)] (f : AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9), Set.MapsTo.{u2, u1} S S' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : S) => S') _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) T S S' (SMulZeroClass.toSMul.{u3, u2} T S (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))))) (DistribSMul.toSMulZeroClass.{u3, u2} T S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))))) (DistribMulAction.toDistribSMul.{u3, u2} T S (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))))) (Module.toDistribMulAction.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))) (Algebra.toModule.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) _inst_6))))) (SMulZeroClass.toSMul.{u3, u1} T S' (AddMonoid.toZero.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))))) (DistribSMul.toSMulZeroClass.{u3, u1} T S' (AddMonoid.toAddZeroClass.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))))) (DistribMulAction.toDistribSMul.{u3, u1} T S' (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)))))) (Module.toDistribMulAction.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))) (Algebra.toModule.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) T S S' (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)))))) (Module.toDistribMulAction.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))) (Algebra.toModule.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) _inst_6)) (Module.toDistribMulAction.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))) (Algebra.toModule.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_9)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) T S S' (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)))) (Module.toDistribMulAction.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))) (Algebra.toModule.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) _inst_6)) (Module.toDistribMulAction.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))) (Algebra.toModule.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_9)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9 (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) (AlgHom.algHomClass.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9))))) f) (Polynomial.rootSet.{u3, u2} T _inst_3 p S _inst_4 _inst_5 _inst_6) (Polynomial.rootSet.{u3, u1} T _inst_3 p S' _inst_7 _inst_8 _inst_9)
 Case conversion may be inaccurate. Consider using '#align polynomial.root_set_maps_to Polynomial.rootSet_mapsToₓ'. -/
 theorem rootSet_mapsTo {p : T[X]} {S S'} [CommRing S] [IsDomain S] [Algebra T S] [CommRing S']
     [IsDomain S'] [Algebra T S'] [NoZeroSMulDivisors T S'] (f : S →ₐ[T] S') :

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

@@ -339,7 +339,7 @@ theorem degree_coe_units [Nontrivial R] (u : R[X]ˣ) : degree (u : R[X]) = 0 :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {p : Polynomial.{u1} R _inst_1}, Iff (IsUnit.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) p) (Exists.{succ u1} R (fun (r : R) => And (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) r) (Eq.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) r) p)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R _inst_1}, Iff (IsUnit.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) p) (Exists.{succ u1} R (fun (r : R) => And (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) r) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r) p)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R _inst_1}, Iff (IsUnit.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) p) (Exists.{succ u1} R (fun (r : R) => And (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) r) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r) p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.is_unit_iff Polynomial.isUnit_iffₓ'. -/
 theorem isUnit_iff : IsUnit p ↔ ∃ r : R, IsUnit r ∧ C r = p :=
   ⟨fun hp =>
@@ -515,7 +515,7 @@ variable [CommRing R]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (forall {a : R} {n : Nat}, Iff (LE.le.{0} Nat Nat.hasLe n (Polynomial.rootMultiplicity.{u1} R _inst_1 a p)) (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) n) p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) -> (forall {a : R} {n : Nat}, Iff (LE.le.{0} Nat instLENat n (Polynomial.rootMultiplicity.{u1} R _inst_1 a p)) (Dvd.dvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) n) p))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) -> (forall {a : R} {n : Nat}, Iff (LE.le.{0} Nat instLENat n (Polynomial.rootMultiplicity.{u1} R _inst_1 a p)) (Dvd.dvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) n) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.le_root_multiplicity_iff Polynomial.le_rootMultiplicity_iffₓ'. -/
 /-- The multiplicity of `a` as root of a nonzero polynomial `p` is at least `n` iff
   `(X - a) ^ n` divides `p`. -/
@@ -533,7 +533,7 @@ theorem le_rootMultiplicity_iff {p : R[X]} (p0 : p ≠ 0) {a : R} {n : ℕ} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (forall (a : R) (n : Nat), Iff (LE.le.{0} Nat Nat.hasLe (Polynomial.rootMultiplicity.{u1} R _inst_1 a p) n) (Not (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) p)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) -> (forall (a : R) (n : Nat), Iff (LE.le.{0} Nat instLENat (Polynomial.rootMultiplicity.{u1} R _inst_1 a p) n) (Not (Dvd.dvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p)))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) -> (forall (a : R) (n : Nat), Iff (LE.le.{0} Nat instLENat (Polynomial.rootMultiplicity.{u1} R _inst_1 a p) n) (Not (Dvd.dvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.root_multiplicity_le_iff Polynomial.rootMultiplicity_le_iffₓ'. -/
 theorem rootMultiplicity_le_iff {p : R[X]} (p0 : p ≠ 0) (a : R) (n : ℕ) :
     rootMultiplicity a p ≤ n ↔ ¬(X - C a) ^ (n + 1) ∣ p := by
@@ -544,7 +544,7 @@ theorem rootMultiplicity_le_iff {p : R[X]} (p0 : p ≠ 0) (a : R) (n : ℕ) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (forall (a : R), Not (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Polynomial.rootMultiplicity.{u1} R _inst_1 a p) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) -> (forall (a : R), Not (Dvd.dvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Polynomial.rootMultiplicity.{u1} R _inst_1 a p) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) -> (forall (a : R), Not (Dvd.dvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Polynomial.rootMultiplicity.{u1} R _inst_1 a p) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.pow_root_multiplicity_not_dvd Polynomial.pow_rootMultiplicity_not_dvdₓ'. -/
 theorem pow_rootMultiplicity_not_dvd {p : R[X]} (p0 : p ≠ 0) (a : R) :
     ¬(X - C a) ^ (rootMultiplicity a p + 1) ∣ p := by rw [← root_multiplicity_le_iff p0]
@@ -576,7 +576,7 @@ open Multiset
 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))] (r : R), Prime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) r))
 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))] (r : R), Prime.{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))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{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))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) r))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (r : R), Prime.{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))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{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))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) r))
 Case conversion may be inaccurate. Consider using '#align polynomial.prime_X_sub_C Polynomial.prime_X_sub_Cₓ'. -/
 theorem prime_X_sub_C (r : R) : Prime (X - C r) :=
   ⟨X_sub_C_ne_zero r, not_isUnit_X_sub_C r, fun _ _ =>
@@ -604,7 +604,7 @@ theorem Monic.prime_of_degree_eq_one (hp1 : degree p = 1) (hm : Monic p) : Prime
 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))] (r : R), Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) r))
 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))] (r : R), Irreducible.{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))) (Semiring.toMonoidWithZero.{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))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{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))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) r))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (r : R), Irreducible.{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))) (Semiring.toMonoidWithZero.{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))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{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))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) r))
 Case conversion may be inaccurate. Consider using '#align polynomial.irreducible_X_sub_C Polynomial.irreducible_X_sub_Cₓ'. -/
 theorem irreducible_X_sub_C (r : R) : Irreducible (X - C r) :=
   (prime_X_sub_C r).Irreducible
@@ -662,7 +662,7 @@ theorem rootMultiplicity_mul {p q : R[X]} {x : R} (hpq : p * q ≠ 0) :
 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))] {x : R}, Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 x (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) x))) (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))] {x : R}, Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 x (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) x) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) x))) (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))] {x : R}, Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 x (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) x) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) x))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))
 Case conversion may be inaccurate. Consider using '#align polynomial.root_multiplicity_X_sub_C_self Polynomial.rootMultiplicity_X_sub_C_selfₓ'. -/
 theorem rootMultiplicity_X_sub_C_self {x : R} : rootMultiplicity x (X - C x) = 1 := by
   rw [root_multiplicity_eq_multiplicity, dif_neg (X_sub_C_ne_zero x),
@@ -673,7 +673,7 @@ theorem rootMultiplicity_X_sub_C_self {x : R} : rootMultiplicity x (X - C x) = 1
 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))] {x : R} {y : R}, Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 x (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) y))) (ite.{1} Nat (Eq.{succ u1} R x y) (Classical.propDecidable (Eq.{succ u1} R x y)) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {x : R} {y : R}, Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 x (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) y) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) y))) (ite.{1} Nat (Eq.{succ u1} R x y) (Classical.propDecidable (Eq.{succ u1} R x y)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {x : R} {y : R}, Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 x (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) y) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) y))) (ite.{1} Nat (Eq.{succ u1} R x y) (Classical.propDecidable (Eq.{succ u1} R x y)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))
 Case conversion may be inaccurate. Consider using '#align polynomial.root_multiplicity_X_sub_C Polynomial.rootMultiplicity_X_sub_Cₓ'. -/
 theorem rootMultiplicity_X_sub_C {x y : R} :
     rootMultiplicity x (X - C y) = if x = y then 1 else 0 :=
@@ -688,7 +688,7 @@ theorem rootMultiplicity_X_sub_C {x y : 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))] (a : R) (n : Nat), Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 a (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) n)) n
 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))] (a : R) (n : Nat), Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 a (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) n)) n
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (a : R) (n : Nat), Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 a (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) n)) n
 Case conversion may be inaccurate. Consider using '#align polynomial.root_multiplicity_X_sub_C_pow Polynomial.rootMultiplicity_X_sub_C_powₓ'. -/
 /-- The multiplicity of `a` as root of `(X - a) ^ n` is `n`. -/
 theorem rootMultiplicity_X_sub_C_pow (a : R) (n : ℕ) : rootMultiplicity a ((X - C a) ^ n) = n :=
@@ -794,7 +794,7 @@ theorem card_roots' (p : R[X]) : p.roots.card ≤ natDegree p :=
 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {a : R}, (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 (CommRing.toRing.{u1} R _inst_1)) p)) -> (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))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a))))) (Polynomial.degree.{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))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {a : R}, (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 (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (FunLike.coe.{succ u1, succ u1, 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(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))) a))))) (Polynomial.degree.{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))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {a : R}, (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 (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (FunLike.coe.{succ u1, succ u1, 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(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))) a))))) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.card_roots_sub_C Polynomial.card_roots_sub_Cₓ'. -/
 theorem card_roots_sub_C {p : R[X]} {a : R} (hp0 : 0 < degree p) :
     ((p - C a).roots.card : WithBot ℕ) ≤ degree p :=
@@ -809,7 +809,7 @@ theorem card_roots_sub_C {p : R[X]} {a : R} (hp0 : 0 < degree p) :
 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {a : R}, (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 (CommRing.toRing.{u1} R _inst_1)) p)) -> (LE.le.{0} Nat Nat.hasLe (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a)))) (Polynomial.natDegree.{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))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {a : R}, (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 (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) -> (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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 (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (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))) a)))) instLENat (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a)))) (Polynomial.natDegree.{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))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {a : R}, (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 (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) -> (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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 (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (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))) a)))) instLENat (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a)))) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.card_roots_sub_C' Polynomial.card_roots_sub_C'ₓ'. -/
 theorem card_roots_sub_C' {p : R[X]} {a : R} (hp0 : 0 < degree p) :
     (p - C a).roots.card ≤ natDegree p :=
@@ -925,7 +925,7 @@ theorem roots.le_of_dvd (h : q ≠ 0) : p ∣ q → roots p ≤ roots q :=
 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {a : R} {x : R}, Iff (Membership.Mem.{u1, u1} R (Multiset.{u1} R) (Multiset.hasMem.{u1} R) x (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a)))) (And (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a)) (Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x p) a))
 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))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {a : R} {x : R}, Iff (Membership.mem.{u1, u1} R (Multiset.{u1} R) (Multiset.instMembershipMultiset.{u1} R) x (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a)))) (And (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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 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_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))) a)) (Eq.{succ u1} R (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) x p) a))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {a : R} {x : R}, Iff (Membership.mem.{u1, u1} R (Multiset.{u1} R) (Multiset.instMembershipMultiset.{u1} R) x (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a)))) (And (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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))) a)) (Eq.{succ u1} R (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) x p) a))
 Case conversion may be inaccurate. Consider using '#align polynomial.mem_roots_sub_C' Polynomial.mem_roots_sub_C'ₓ'. -/
 theorem mem_roots_sub_C' {p : R[X]} {a x : R} : x ∈ (p - C a).roots ↔ p ≠ C a ∧ p.eval x = a := by
   rw [mem_roots', is_root.def, sub_ne_zero, eval_sub, sub_eq_zero, eval_C]
@@ -935,7 +935,7 @@ theorem mem_roots_sub_C' {p : R[X]} {a x : R} : x ∈ (p - C a).roots ↔ p ≠
 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {a : R} {x : R}, (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 (CommRing.toRing.{u1} R _inst_1)) p)) -> (Iff (Membership.Mem.{u1, u1} R (Multiset.{u1} R) (Multiset.hasMem.{u1} R) x (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a)))) (Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x p) a))
 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))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {a : R} {x : R}, (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 (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) -> (Iff (Membership.mem.{u1, u1} R (Multiset.{u1} R) (Multiset.instMembershipMultiset.{u1} R) x (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a)))) (Eq.{succ u1} R (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) x p) a))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {a : R} {x : R}, (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 (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) -> (Iff (Membership.mem.{u1, u1} R (Multiset.{u1} R) (Multiset.instMembershipMultiset.{u1} R) x (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a)))) (Eq.{succ u1} R (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) x p) a))
 Case conversion may be inaccurate. Consider using '#align polynomial.mem_roots_sub_C Polynomial.mem_roots_sub_Cₓ'. -/
 theorem mem_roots_sub_C {p : R[X]} {a x : R} (hp0 : 0 < degree p) :
     x ∈ (p - C a).roots ↔ p.eval x = a :=
@@ -946,7 +946,7 @@ theorem mem_roots_sub_C {p : R[X]} {a x : R} (hp0 : 0 < degree p) :
 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))] (r : R), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) r))) (Singleton.singleton.{u1, u1} R (Multiset.{u1} R) (Multiset.hasSingleton.{u1} R) r)
 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))] (r : R), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{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))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) r))) (Singleton.singleton.{u1, u1} R (Multiset.{u1} R) (Multiset.instSingletonMultiset.{u1} R) r)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (r : R), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{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))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) r))) (Singleton.singleton.{u1, u1} R (Multiset.{u1} R) (Multiset.instSingletonMultiset.{u1} R) r)
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_X_sub_C Polynomial.roots_X_sub_Cₓ'. -/
 @[simp]
 theorem roots_X_sub_C (r : R) : roots (X - C r) = {r} :=
@@ -969,7 +969,7 @@ theorem roots_X : roots (X : R[X]) = {0} := by rw [← roots_X_sub_C, C_0, sub_z
 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))] (x : R), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (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))) x)) (OfNat.ofNat.{u1} (Multiset.{u1} R) 0 (OfNat.mk.{u1} (Multiset.{u1} R) 0 (Zero.zero.{u1} (Multiset.{u1} R) (Multiset.hasZero.{u1} R))))
 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))] (x : R), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (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))) x)) (OfNat.ofNat.{u1} (Multiset.{u1} R) 0 (Zero.toOfNat0.{u1} (Multiset.{u1} R) (Multiset.instZeroMultiset.{u1} R)))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (x : R), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (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))) x)) (OfNat.ofNat.{u1} (Multiset.{u1} R) 0 (Zero.toOfNat0.{u1} (Multiset.{u1} R) (Multiset.instZeroMultiset.{u1} R)))
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_C Polynomial.roots_Cₓ'. -/
 @[simp]
 theorem roots_C (x : R) : (C x).roots = 0 :=
@@ -990,7 +990,7 @@ theorem roots_one : (1 : R[X]).roots = ∅ :=
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{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 (CommRing.toRing.{u1} R _inst_1)))))))))) -> (Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HMul.hMul.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (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))) a) p)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))) -> (Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (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))) a) p)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))) -> (Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (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))) a) p)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_C_mul Polynomial.roots_C_mulₓ'. -/
 @[simp]
 theorem roots_C_mul (p : R[X]) (ha : a ≠ 0) : (C a * p).roots = p.roots := by
@@ -1073,7 +1073,7 @@ theorem roots_X_pow (n : ℕ) : (X ^ n : R[X]).roots = n • {0} := by rw [roots
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{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 (CommRing.toRing.{u1} R _inst_1)))))))))) -> (forall (n : Nat), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HMul.hMul.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (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))) a) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) n))) (SMul.smul.{0, u1} Nat (Multiset.{u1} R) (AddMonoid.SMul.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) n (Singleton.singleton.{u1, u1} R (Multiset.{u1} R) (Multiset.hasSingleton.{u1} R) (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 (CommRing.toRing.{u1} R _inst_1))))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))], (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))) -> (forall (n : Nat), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (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))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (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))) a) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n))) (HSMul.hSMul.{0, u1, u1} Nat (Multiset.{u1} R) (Multiset.{u1} R) (instHSMul.{0, u1} Nat (Multiset.{u1} R) (AddMonoid.SMul.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) n (Singleton.singleton.{u1, u1} R (Multiset.{u1} R) (Multiset.instSingletonMultiset.{u1} R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))))))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))], (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))) -> (forall (n : Nat), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (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))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (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))) a) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n))) (HSMul.hSMul.{0, u1, u1} Nat (Multiset.{u1} R) (Multiset.{u1} R) (instHSMul.{0, u1} Nat (Multiset.{u1} R) (AddMonoid.SMul.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) n (Singleton.singleton.{u1, u1} R (Multiset.{u1} R) (Multiset.instSingletonMultiset.{u1} R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_C_mul_X_pow Polynomial.roots_C_mul_X_powₓ'. -/
 theorem roots_C_mul_X_pow (ha : a ≠ 0) (n : ℕ) : (C a * X ^ n).roots = n • {0} := by
   rw [roots_C_mul _ ha, roots_X_pow]
@@ -1094,7 +1094,7 @@ theorem roots_monomial (ha : a ≠ 0) (n : ℕ) : (monomial n a).roots = n • {
 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))] (s : Finset.{u1} R), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (Finset.prod.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) s (fun (a : R) => HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)))) (Finset.val.{u1} R s)
 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))] (s : Finset.{u1} R), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (Finset.prod.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) s (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)))) (Finset.val.{u1} R s)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (s : Finset.{u1} R), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (Finset.prod.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) s (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)))) (Finset.val.{u1} R s)
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_prod_X_sub_C Polynomial.roots_prod_X_sub_Cₓ'. -/
 theorem roots_prod_X_sub_C (s : Finset R) : (s.Prod fun a => X - C a).roots = s.val :=
   (roots_prod (fun a => X - C a) s (prod_ne_zero_iff.mpr fun a _ => X_sub_C_ne_zero a)).trans
@@ -1105,7 +1105,7 @@ theorem roots_prod_X_sub_C (s : Finset R) : (s.Prod fun a => X - C a).roots = s.
 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))] (s : Multiset.{u1} R), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) s))) s
 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))] (s : Multiset.{u1} R), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) s))) s
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (s : Multiset.{u1} R), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) s))) s
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_multiset_prod_X_sub_C Polynomial.roots_multiset_prod_X_sub_Cₓ'. -/
 @[simp]
 theorem roots_multiset_prod_X_sub_C (s : Multiset R) : (s.map fun a => X - C a).Prod.roots = s :=
@@ -1121,7 +1121,7 @@ theorem roots_multiset_prod_X_sub_C (s : Multiset R) : (s.map fun a => X - C a).
 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))] (s : Multiset.{u1} R), Eq.{1} Nat (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) s))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s)
 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))] (s : Multiset.{u1} R), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) s))) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (s : Multiset.{u1} R), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) s))) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s)
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_multiset_prod_X_sub_C_eq_card Polynomial.natDegree_multiset_prod_X_sub_C_eq_cardₓ'. -/
 @[simp]
 theorem natDegree_multiset_prod_X_sub_C_eq_card (s : Multiset R) :
@@ -1138,7 +1138,7 @@ theorem natDegree_multiset_prod_X_sub_C_eq_card (s : Multiset 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))] {n : Nat}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n) -> (forall (a : R), LE.le.{0} Nat Nat.hasLe (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) n) (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))) a)))) n)
 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))] {n : Nat}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) -> (forall (a : R), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n) (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 (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (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))) a)))) instLENat (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n) (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))) a)))) n)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {n : Nat}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) -> (forall (a : R), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n) (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 (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (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))) a)))) instLENat (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n) (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))) a)))) n)
 Case conversion may be inaccurate. Consider using '#align polynomial.card_roots_X_pow_sub_C Polynomial.card_roots_X_pow_sub_Cₓ'. -/
 theorem card_roots_X_pow_sub_C {n : ℕ} (hn : 0 < n) (a : R) :
     (roots ((X : R[X]) ^ n - C a)).card ≤ n :=
@@ -1247,7 +1247,7 @@ theorem Monic.comp (hp : p.Monic) (hq : q.Monic) (h : q.natDegree ≠ 0) : (p.co
 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))] {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) -> (forall (r : R), Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.comp.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p (HAdd.hAdd.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) r))))
 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))] {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) -> (forall (r : R), Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{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))) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) r))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {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) -> (forall (r : R), Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{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))) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) r))))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic.comp_X_add_C Polynomial.Monic.comp_X_add_Cₓ'. -/
 theorem Monic.comp_X_add_C (hp : p.Monic) (r : R) : (p.comp (X + C r)).Monic :=
   by
@@ -1260,7 +1260,7 @@ theorem Monic.comp_X_add_C (hp : p.Monic) (r : R) : (p.comp (X + C r)).Monic :=
 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))] {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) -> (forall (r : R), Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.comp.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) r))))
 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))] {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) -> (forall (r : R), Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{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))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) r))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {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) -> (forall (r : R), Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{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))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) r))))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic.comp_X_sub_C Polynomial.Monic.comp_X_sub_Cₓ'. -/
 theorem Monic.comp_X_sub_C (hp : p.Monic) (r : R) : (p.comp (X - C r)).Monic := by
   simpa using hp.comp_X_add_C (-r)
@@ -1291,7 +1291,7 @@ theorem natDegree_coe_units (u : R[X]ˣ) : natDegree (u : R[X]) = 0 :=
 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Iff (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.comp.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p q) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Or (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (And (Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) q (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) p) (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 (CommRing.toRing.{u1} R _inst_1)))))))))) (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) q (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))) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) q (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, Iff (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p q) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Or (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (And (Eq.{succ u1} R (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) q (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) p) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))) (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) q (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))) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) q (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, Iff (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p q) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Or (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (And (Eq.{succ u1} R (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) q (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) p) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))) (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) q (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))) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) q (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.comp_eq_zero_iff Polynomial.comp_eq_zero_iffₓ'. -/
 theorem comp_eq_zero_iff : p.comp q = 0 ↔ p = 0 ∨ p.eval (q.coeff 0) = 0 ∧ q = C (q.coeff 0) :=
   by
@@ -1360,7 +1360,7 @@ theorem rootSet_def (p : T[X]) (S) [CommRing S] [IsDomain S] [Algebra T S] :
 lean 3 declaration is
   forall {S : Type.{u1}} {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))] (a : T), Eq.{succ u1} (Set.{u1} S) (Polynomial.rootSet.{u2, u1} T _inst_3 (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} T (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))))) (fun (_x : RingHom.{u2, u2} T (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))))) => T -> (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3)))) (RingHom.hasCoeToFun.{u2, u2} T (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))))) (Polynomial.C.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) a) S _inst_4 _inst_5 _inst_6) (EmptyCollection.emptyCollection.{u1} (Set.{u1} S) (Set.hasEmptyc.{u1} S))
 but is expected to have type
-  forall {S : Type.{u1}} {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))] (a : T), Eq.{succ u1} (Set.{u1} S) (Polynomial.rootSet.{u2, u1} T _inst_3 (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) T (fun (_x : T) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : T) => Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (Polynomial.C.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) a) S _inst_4 _inst_5 _inst_6) (EmptyCollection.emptyCollection.{u1} (Set.{u1} S) (Set.instEmptyCollectionSet.{u1} S))
+  forall {S : Type.{u1}} {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))] (a : T), Eq.{succ u1} (Set.{u1} S) (Polynomial.rootSet.{u2, u1} T _inst_3 (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) T (fun (_x : T) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : T) => Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (Polynomial.C.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) a) S _inst_4 _inst_5 _inst_6) (EmptyCollection.emptyCollection.{u1} (Set.{u1} S) (Set.instEmptyCollectionSet.{u1} S))
 Case conversion may be inaccurate. Consider using '#align polynomial.root_set_C Polynomial.rootSet_Cₓ'. -/
 @[simp]
 theorem rootSet_C [CommRing S] [IsDomain S] [Algebra T S] (a : T) : (C a).rootSet S = ∅ := by
@@ -1568,7 +1568,7 @@ theorem leadingCoeff_divByMonic_of_monic {R : Type u} [CommRing R] {p q : 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))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Ne.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{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))))) -> (forall (a : R), Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.divByMonic.{u1} R (CommRing.toRing.{u1} R _inst_1) p (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)))) (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))] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), (Ne.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{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))))) -> (forall (a : R), Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.divByMonic.{u1} R (CommRing.toRing.{u1} R _inst_1) p (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)))) (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))] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), (Ne.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{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))))) -> (forall (a : R), Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.divByMonic.{u1} R (CommRing.toRing.{u1} R _inst_1) p (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)))) (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_div_by_monic_X_sub_C Polynomial.leadingCoeff_divByMonic_X_sub_Cₓ'. -/
 theorem leadingCoeff_divByMonic_X_sub_C (p : R[X]) (hp : degree p ≠ 0) (a : R) :
     leadingCoeff (p /ₘ (X - C a)) = leadingCoeff p :=
@@ -1584,7 +1584,7 @@ theorem leadingCoeff_divByMonic_X_sub_C (p : R[X]) (hp : degree p ≠ 0) (a : R)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) p) -> (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.commRing.{u1} R _inst_3))))))) p q) -> (LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) q) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) p)) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) q (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) q)) p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))}, (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) p) -> (Dvd.dvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (semigroupDvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.commRing.{u1} R _inst_3))))))) p q) -> (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) q) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) p)) -> (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) q (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) q)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) q)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) q)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) 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_3))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) q)) p))
+  forall {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))}, (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) p) -> (Dvd.dvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (semigroupDvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.commRing.{u1} R _inst_3))))))) p q) -> (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) q) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) p)) -> (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) q (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) q)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) q)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) q)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) 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_3))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) q)) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_leading_coeff_mul_of_monic_of_dvd_of_nat_degree_le Polynomial.eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_leₓ'. -/
 theorem eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le {R} [CommRing R] {p q : R[X]}
     (hp : p.Monic) (hdiv : p ∣ q) (hdeg : q.natDegree ≤ p.natDegree) : q = C q.leadingCoeff * p :=
@@ -1615,7 +1615,7 @@ theorem eq_of_monic_of_dvd_of_natDegree_le {R} [CommRing R] {p q : R[X]} (hp : p
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {a : R} {b : R}, (IsUnit.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_3)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_3))))))) a b)) -> (IsCoprime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) a)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) b)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {a : R} {b : R}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_3))) a b)) -> (IsCoprime.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) 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_3))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) a)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) b) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) 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_3))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) b)))
+  forall {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {a : R} {b : R}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_3))) a b)) -> (IsCoprime.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) 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_3))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) a)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) b) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) 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_3))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) b)))
 Case conversion may be inaccurate. Consider using '#align polynomial.is_coprime_X_sub_C_of_is_unit_sub Polynomial.isCoprime_X_sub_C_of_isUnit_subₓ'. -/
 theorem isCoprime_X_sub_C_of_isUnit_sub {R} [CommRing R] {a b : R} (h : IsUnit (a - b)) :
     IsCoprime (X - C a) (X - C b) :=
@@ -1630,7 +1630,7 @@ theorem isCoprime_X_sub_C_of_isUnit_sub {R} [CommRing R] {a b : R} (h : IsUnit (
 lean 3 declaration is
   forall {K : Type.{u2}} [_inst_3 : Field.{u2} K] {I : Type.{u1}} {s : I -> K}, (Function.Injective.{succ u1, succ u2} I K s) -> (Pairwise.{u1} I (Function.onFun.{succ u1, succ u2, 1} I (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) Prop (IsCoprime.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (Polynomial.commSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_3)))) (fun (i : I) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (instHSub.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (Polynomial.sub.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (Polynomial.X.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))))) (fun (_x : RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))))) => K -> (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) (RingHom.hasCoeToFun.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))))) (Polynomial.C.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (s i)))))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_3 : Field.{u1} K] {I : Type.{u2}} {s : I -> K}, (Function.Injective.{succ u2, succ u1} I K s) -> (Pairwise.{u2} I (Function.onFun.{succ u2, succ u1, 1} I (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) Prop (IsCoprime.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Polynomial.commSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (fun (i : I) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) ((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_3)))) (s i)) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (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_3)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) 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_3)))) _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_3)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (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_3)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))))) (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_3)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) (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_3)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (s i)))))
+  forall {K : Type.{u1}} [_inst_3 : Field.{u1} K] {I : Type.{u2}} {s : I -> K}, (Function.Injective.{succ u2, succ u1} I K s) -> (Pairwise.{u2} I (Function.onFun.{succ u2, succ u1, 1} I (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) Prop (IsCoprime.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Polynomial.commSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (fun (i : I) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) ((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_3)))) (s i)) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (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_3)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) 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_3)))) _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_3)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (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_3)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))))) (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_3)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) (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_3)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (s i)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.pairwise_coprime_X_sub_C Polynomial.pairwise_coprime_X_sub_Cₓ'. -/
 theorem pairwise_coprime_X_sub_C {K} [Field K] {I : Type v} {s : I → K} (H : Function.Injective s) :
     Pairwise (IsCoprime on fun i : I => X - C (s i)) := fun i j hij =>
@@ -1641,7 +1641,7 @@ theorem pairwise_coprime_X_sub_C {K} [Field K] {I : Type v} {s : I → K} (H : F
 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))] {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)) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (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))] {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)) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) (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))] {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)) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic_prod_multiset_X_sub_C Polynomial.monic_prod_multiset_X_sub_Cₓ'. -/
 theorem monic_prod_multiset_X_sub_C : Monic (p.roots.map fun a => X - C a).Prod :=
   monic_multiset_prod_of_monic _ _ fun a _ => monic_X_sub_C a
@@ -1651,7 +1651,7 @@ theorem monic_prod_multiset_X_sub_C : Monic (p.roots.map fun a => X - C a).Prod
 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))] {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))) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))) (Finset.prod.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.toFinset.{u1} R (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (fun (a : R) => HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (Polynomial.rootMultiplicity.{u1} R _inst_1 a 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))] {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))) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))) (Finset.prod.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.toFinset.{u1} R (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (fun (a : R) => HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) (Polynomial.rootMultiplicity.{u1} R _inst_1 a 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))] {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))) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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 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(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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))) (Finset.prod.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.toFinset.{u1} R (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (fun (a : R) => HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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} 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 Case conversion may be inaccurate. Consider using '#align polynomial.prod_multiset_root_eq_finset_root Polynomial.prod_multiset_root_eq_finset_rootₓ'. -/
 theorem prod_multiset_root_eq_finset_root :
     (p.roots.map fun a => X - C a).Prod =
@@ -1663,7 +1663,7 @@ theorem prod_multiset_root_eq_finset_root :
 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))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 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))] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), Dvd.dvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 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))] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), Dvd.dvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))) p
 Case conversion may be inaccurate. Consider using '#align polynomial.prod_multiset_X_sub_C_dvd Polynomial.prod_multiset_X_sub_C_dvdₓ'. -/
 /-- The product `∏ (X - a)` for `a` inside the multiset `p.roots` divides `p`. -/
 theorem prod_multiset_X_sub_C_dvd (p : R[X]) : (p.roots.map fun a => X - C a).Prod ∣ p :=
@@ -1680,7 +1680,7 @@ theorem prod_multiset_X_sub_C_dvd (p : R[X]) : (p.roots.map fun a => X - C a).Pr
 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (forall (s : Multiset.{u1} R), Iff (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) s)) p) (LE.le.{u1} (Multiset.{u1} R) (Preorder.toHasLe.{u1} (Multiset.{u1} R) (PartialOrder.toPreorder.{u1} (Multiset.{u1} R) (Multiset.partialOrder.{u1} R))) s (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))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) -> (forall (s : Multiset.{u1} R), Iff (Dvd.dvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) s)) p) (LE.le.{u1} (Multiset.{u1} R) (Preorder.toLE.{u1} (Multiset.{u1} R) (PartialOrder.toPreorder.{u1} (Multiset.{u1} R) (Multiset.instPartialOrderMultiset.{u1} R))) s (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))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) -> (forall (s : Multiset.{u1} R), Iff (Dvd.dvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) s)) p) (LE.le.{u1} (Multiset.{u1} R) (Preorder.toLE.{u1} (Multiset.{u1} R) (PartialOrder.toPreorder.{u1} (Multiset.{u1} R) (Multiset.instPartialOrderMultiset.{u1} R))) s (Polynomial.roots.{u1} R _inst_1 _inst_2 p)))
 Case conversion may be inaccurate. Consider using '#align multiset.prod_X_sub_C_dvd_iff_le_roots Multiset.prod_X_sub_C_dvd_iff_le_rootsₓ'. -/
 /-- A Galois connection. -/
 theorem Multiset.prod_X_sub_C_dvd_iff_le_roots {p : R[X]} (hp : p ≠ 0) (s : Multiset R) :
@@ -1699,7 +1699,7 @@ theorem Multiset.prod_X_sub_C_dvd_iff_le_roots {p : R[X]} (hp : p ≠ 0) (s : Mu
 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))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), Exists.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => And (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))) q) p) (And (Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) q)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) (Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 q) (OfNat.ofNat.{u1} (Multiset.{u1} R) 0 (OfNat.mk.{u1} (Multiset.{u1} R) 0 (Zero.zero.{u1} (Multiset.{u1} R) (Multiset.hasZero.{u1} R)))))))
 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))] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => And (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (HMul.hMul.{u1, 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))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))) q) p) (And (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) instAddNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) q)) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) (Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 q) (OfNat.ofNat.{u1} (Multiset.{u1} R) 0 (Zero.toOfNat0.{u1} (Multiset.{u1} R) (Multiset.instZeroMultiset.{u1} R))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => And (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (HMul.hMul.{u1, 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))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))) q) p) (And (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) instAddNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) q)) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) (Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 q) (OfNat.ofNat.{u1} (Multiset.{u1} R) 0 (Zero.toOfNat0.{u1} (Multiset.{u1} R) (Multiset.instZeroMultiset.{u1} R))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.exists_prod_multiset_X_sub_C_mul Polynomial.exists_prod_multiset_X_sub_C_mulₓ'. -/
 theorem exists_prod_multiset_X_sub_C_mul (p : R[X]) :
     ∃ q,
@@ -1724,7 +1724,7 @@ theorem exists_prod_multiset_X_sub_C_mul (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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Eq.{1} Nat (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{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))) (HMul.hMul.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (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))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 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))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (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))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) (Multiset.prod.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) (CommRing.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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 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(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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 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))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (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 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(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))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) (Multiset.prod.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) (CommRing.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)))) p)
 Case conversion may be inaccurate. Consider using '#align polynomial.C_leading_coeff_mul_prod_multiset_X_sub_C Polynomial.C_leadingCoeff_mul_prod_multiset_X_sub_Cₓ'. -/
 /-- A polynomial `p` that has as many roots as its degree
 can be written `p = p.leading_coeff * ∏(X - a)`, for `a` in `p.roots`. -/
@@ -1739,7 +1739,7 @@ theorem C_leadingCoeff_mul_prod_multiset_X_sub_C (hroots : p.roots.card = p.natD
 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))] {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.{1} Nat (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{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))) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 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))] {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.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) -> (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 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))] {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.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) -> (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))) p)
 Case conversion may be inaccurate. Consider using '#align polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq Polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eqₓ'. -/
 /-- A monic polynomial `p` that has as many roots as its degree
 can be written `p = ∏(X - a)`, for `a` in `p.roots`. -/
@@ -1760,7 +1760,7 @@ variable {A B : Type _} [CommRing A] [CommRing B]
 lean 3 declaration is
   forall {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommRing.{u1} A] [_inst_2 : CommRing.{u2} B] {p : Polynomial.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))} {f : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))}, (Ne.{succ u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p) (OfNat.ofNat.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) 0 (OfNat.mk.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) 0 (Zero.zero.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) (Polynomial.zero.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))))))) -> (forall (a : A), LE.le.{0} Nat Nat.hasLe (Polynomial.rootMultiplicity.{u1} A _inst_1 a p) (Polynomial.rootMultiplicity.{u2} B _inst_2 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f a) (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p)))
 but is expected to have type
-  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] {p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))} {f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))}, (Ne.{succ u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p) (OfNat.ofNat.{u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (Polynomial.zero.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))))) -> (forall (a : A), LE.le.{0} Nat instLENat (Polynomial.rootMultiplicity.{u2} A _inst_1 a p) (Polynomial.rootMultiplicity.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) _inst_2 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f a) (Polynomial.map.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) _inst_2)) f p)))
+  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] {p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))} {f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))}, (Ne.{succ u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p) (OfNat.ofNat.{u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (Polynomial.zero.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))))) -> (forall (a : A), LE.le.{0} Nat instLENat (Polynomial.rootMultiplicity.{u2} A _inst_1 a p) (Polynomial.rootMultiplicity.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) a) _inst_2 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f a) (Polynomial.map.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) a) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) a) _inst_2)) f p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.le_root_multiplicity_map Polynomial.le_rootMultiplicity_mapₓ'. -/
 theorem le_rootMultiplicity_map {p : A[X]} {f : A →+* B} (hmap : map f p ≠ 0) (a : A) :
     rootMultiplicity a p ≤ rootMultiplicity (f a) (p.map f) :=
@@ -1774,7 +1774,7 @@ theorem le_rootMultiplicity_map {p : A[X]} {f : A →+* B} (hmap : map f p ≠ 0
 lean 3 declaration is
   forall {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommRing.{u1} A] [_inst_2 : CommRing.{u2} B] {p : Polynomial.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))} {f : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))}, (Function.Injective.{succ u1, succ u2} A B (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f)) -> (forall (a : A), Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} A _inst_1 a p) (Polynomial.rootMultiplicity.{u2} B _inst_2 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f a) (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p)))
 but is expected to have type
-  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] {p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))} {f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f)) -> (forall (a : A), Eq.{1} Nat (Polynomial.rootMultiplicity.{u2} A _inst_1 a p) (Polynomial.rootMultiplicity.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) _inst_2 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f a) (Polynomial.map.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) _inst_2)) f p)))
+  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] {p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))} {f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f)) -> (forall (a : A), Eq.{1} Nat (Polynomial.rootMultiplicity.{u2} A _inst_1 a p) (Polynomial.rootMultiplicity.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) a) _inst_2 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f a) (Polynomial.map.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) a) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) a) _inst_2)) f p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_root_multiplicity_map Polynomial.eq_rootMultiplicity_mapₓ'. -/
 theorem eq_rootMultiplicity_map {p : A[X]} {f : A →+* B} (hf : Function.Injective f) (a : A) :
     rootMultiplicity a p = rootMultiplicity (f a) (p.map f) :=
@@ -1790,7 +1790,7 @@ theorem eq_rootMultiplicity_map {p : A[X]} {f : A →+* B} (hf : Function.Inject
 lean 3 declaration is
   forall {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommRing.{u1} A] [_inst_2 : CommRing.{u2} B] [_inst_3 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))] {p : Polynomial.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))} {f : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))}, (Ne.{succ u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p) (OfNat.ofNat.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) 0 (OfNat.mk.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) 0 (Zero.zero.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) (Polynomial.zero.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))))))) -> (forall (b : B), LE.le.{0} Nat Nat.hasLe (Multiset.count.{u2} B (fun (a : B) (b : B) => Classical.propDecidable (Eq.{succ u2} B a b)) b (Multiset.map.{u1, u2} A B (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f) (Polynomial.roots.{u1} A _inst_1 _inst_3 p))) (Polynomial.rootMultiplicity.{u2} B _inst_2 b (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p)))
 but is expected to have type
-  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))] {p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))} {f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))}, (Ne.{succ u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p) (OfNat.ofNat.{u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (Polynomial.zero.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))))) -> (forall (b : B), LE.le.{0} Nat instLENat (Multiset.count.{u1} B (fun (a : B) (b : B) => Classical.propDecidable (Eq.{succ u1} B a b)) b (Multiset.map.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f) (Polynomial.roots.{u2} A _inst_1 _inst_3 p))) (Polynomial.rootMultiplicity.{u1} B _inst_2 b (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p)))
+  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))] {p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))} {f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))}, (Ne.{succ u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p) (OfNat.ofNat.{u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (Polynomial.zero.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))))) -> (forall (b : B), LE.le.{0} Nat instLENat (Multiset.count.{u1} B (fun (a : B) (b : B) => Classical.propDecidable (Eq.{succ u1} B a b)) b (Multiset.map.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f) (Polynomial.roots.{u2} A _inst_1 _inst_3 p))) (Polynomial.rootMultiplicity.{u1} B _inst_2 b (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.count_map_roots Polynomial.count_map_rootsₓ'. -/
 theorem count_map_roots [IsDomain A] {p : A[X]} {f : A →+* B} (hmap : map f p ≠ 0) (b : B) :
     (p.roots.map f).count b ≤ rootMultiplicity b (p.map f) :=
@@ -1809,7 +1809,7 @@ theorem count_map_roots [IsDomain A] {p : A[X]} {f : A →+* B} (hmap : map f p
 lean 3 declaration is
   forall {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommRing.{u1} A] [_inst_2 : CommRing.{u2} B] [_inst_3 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))] (p : Polynomial.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))) {f : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))}, (Function.Injective.{succ u1, succ u2} A B (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f)) -> (forall (b : B), LE.le.{0} Nat Nat.hasLe (Multiset.count.{u2} B (fun (a : B) (b : B) => Classical.propDecidable (Eq.{succ u2} B a b)) b (Multiset.map.{u1, u2} A B (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f) (Polynomial.roots.{u1} A _inst_1 _inst_3 p))) (Polynomial.rootMultiplicity.{u2} B _inst_2 b (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p)))
 but is expected to have type
-  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))] (p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) {f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f)) -> (forall (b : B), LE.le.{0} Nat instLENat (Multiset.count.{u1} B (fun (a : B) (b : B) => Classical.propDecidable (Eq.{succ u1} B a b)) b (Multiset.map.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f) (Polynomial.roots.{u2} A _inst_1 _inst_3 p))) (Polynomial.rootMultiplicity.{u1} B _inst_2 b (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p)))
+  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))] (p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) {f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f)) -> (forall (b : B), LE.le.{0} Nat instLENat (Multiset.count.{u1} B (fun (a : B) (b : B) => Classical.propDecidable (Eq.{succ u1} B a b)) b (Multiset.map.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f) (Polynomial.roots.{u2} A _inst_1 _inst_3 p))) (Polynomial.rootMultiplicity.{u1} B _inst_2 b (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.count_map_roots_of_injective Polynomial.count_map_roots_of_injectiveₓ'. -/
 theorem count_map_roots_of_injective [IsDomain A] (p : A[X]) {f : A →+* B}
     (hf : Function.Injective f) (b : B) : (p.roots.map f).count b ≤ rootMultiplicity b (p.map f) :=
@@ -1825,7 +1825,7 @@ theorem count_map_roots_of_injective [IsDomain A] (p : A[X]) {f : A →+* B}
 lean 3 declaration is
   forall {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommRing.{u1} A] [_inst_2 : CommRing.{u2} B] [_inst_3 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))] [_inst_4 : IsDomain.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))] {p : Polynomial.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))} {f : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))}, (Ne.{succ u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p) (OfNat.ofNat.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) 0 (OfNat.mk.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) 0 (Zero.zero.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) (Polynomial.zero.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))))))) -> (LE.le.{u2} (Multiset.{u2} B) (Preorder.toHasLe.{u2} (Multiset.{u2} B) (PartialOrder.toPreorder.{u2} (Multiset.{u2} B) (Multiset.partialOrder.{u2} B))) (Multiset.map.{u1, u2} A B (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f) (Polynomial.roots.{u1} A _inst_1 _inst_3 p)) (Polynomial.roots.{u2} B _inst_2 _inst_4 (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p)))
 but is expected to have type
-  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))] [_inst_4 : IsDomain.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))] {p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))} {f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))}, (Ne.{succ u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p) (OfNat.ofNat.{u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (Polynomial.zero.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))))) -> (LE.le.{u1} (Multiset.{u1} B) (Preorder.toLE.{u1} (Multiset.{u1} B) (PartialOrder.toPreorder.{u1} (Multiset.{u1} B) (Multiset.instPartialOrderMultiset.{u1} B))) (Multiset.map.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (Polynomial.roots.{u1} B _inst_2 _inst_4 (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p)))
+  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))] [_inst_4 : IsDomain.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))] {p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))} {f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))}, (Ne.{succ u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p) (OfNat.ofNat.{u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (Polynomial.zero.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))))) -> (LE.le.{u1} (Multiset.{u1} B) (Preorder.toLE.{u1} (Multiset.{u1} B) (PartialOrder.toPreorder.{u1} (Multiset.{u1} B) (Multiset.instPartialOrderMultiset.{u1} B))) (Multiset.map.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (Polynomial.roots.{u1} B _inst_2 _inst_4 (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_roots_le Polynomial.map_roots_leₓ'. -/
 theorem map_roots_le [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (h : p.map f ≠ 0) :
     p.roots.map f ≤ (p.map f).roots :=
@@ -1838,7 +1838,7 @@ theorem map_roots_le [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (h : p
 lean 3 declaration is
   forall {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommRing.{u1} A] [_inst_2 : CommRing.{u2} B] [_inst_3 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))] [_inst_4 : IsDomain.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))] (p : Polynomial.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))) {f : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))}, (Function.Injective.{succ u1, succ u2} A B (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f)) -> (LE.le.{u2} (Multiset.{u2} B) (Preorder.toHasLe.{u2} (Multiset.{u2} B) (PartialOrder.toPreorder.{u2} (Multiset.{u2} B) (Multiset.partialOrder.{u2} B))) (Multiset.map.{u1, u2} A B (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f) (Polynomial.roots.{u1} A _inst_1 _inst_3 p)) (Polynomial.roots.{u2} B _inst_2 _inst_4 (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p)))
 but is expected to have type
-  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))] [_inst_4 : IsDomain.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))] (p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) {f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f)) -> (LE.le.{u1} (Multiset.{u1} B) (Preorder.toLE.{u1} (Multiset.{u1} B) (PartialOrder.toPreorder.{u1} (Multiset.{u1} B) (Multiset.instPartialOrderMultiset.{u1} B))) (Multiset.map.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (Polynomial.roots.{u1} B _inst_2 _inst_4 (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p)))
+  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))] [_inst_4 : IsDomain.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))] (p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) {f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f)) -> (LE.le.{u1} (Multiset.{u1} B) (Preorder.toLE.{u1} (Multiset.{u1} B) (PartialOrder.toPreorder.{u1} (Multiset.{u1} B) (Multiset.instPartialOrderMultiset.{u1} B))) (Multiset.map.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (Polynomial.roots.{u1} B _inst_2 _inst_4 (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_roots_le_of_injective Polynomial.map_roots_le_of_injectiveₓ'. -/
 theorem map_roots_le_of_injective [IsDomain A] [IsDomain B] (p : A[X]) {f : A →+* B}
     (hf : Function.Injective f) : p.roots.map f ≤ (p.map f).roots :=
@@ -1864,7 +1864,7 @@ theorem card_roots_le_map [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (
 lean 3 declaration is
   forall {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommRing.{u1} A] [_inst_2 : CommRing.{u2} B] [_inst_3 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))] [_inst_4 : IsDomain.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))] {p : Polynomial.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))} {f : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))}, (Function.Injective.{succ u1, succ u2} A B (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f)) -> (LE.le.{0} Nat Nat.hasLe (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} A) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} A) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} A) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} A) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} A) (Multiset.orderedCancelAddCommMonoid.{u1} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} A) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} A) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} A) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} A) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} A) (Multiset.orderedCancelAddCommMonoid.{u1} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} A) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} A) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} A) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} A) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} A) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} A) (Multiset.orderedCancelAddCommMonoid.{u1} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} A) (Polynomial.roots.{u1} A _inst_1 _inst_3 p)) (coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} (Multiset.{u2} B) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} B) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} B) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} B) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} B) (Multiset.orderedCancelAddCommMonoid.{u2} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} (Multiset.{u2} B) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} B) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} B) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} B) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} B) (Multiset.orderedCancelAddCommMonoid.{u2} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u2} B) -> Nat) (AddMonoidHom.hasCoeToFun.{u2, 0} (Multiset.{u2} B) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} B) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} B) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} B) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} B) (Multiset.orderedCancelAddCommMonoid.{u2} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u2} B) (Polynomial.roots.{u2} B _inst_2 _inst_4 (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p))))
 but is expected to have type
-  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))] [_inst_4 : IsDomain.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))] {p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))} {f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f)) -> (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} A) => Nat) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) instLENat (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) (fun (_x : Multiset.{u2} A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} A) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} A) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} A) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} B) (fun (_x : Multiset.{u1} B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} B) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} B) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} B) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} B) (Polynomial.roots.{u1} B _inst_2 _inst_4 (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p))))
+  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))] [_inst_4 : IsDomain.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))] {p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))} {f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f)) -> (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} A) => Nat) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) instLENat (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) (fun (_x : Multiset.{u2} A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} A) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} A) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} A) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} B) (fun (_x : Multiset.{u1} B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} B) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} B) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} B) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} B) (Polynomial.roots.{u1} B _inst_2 _inst_4 (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p))))
 Case conversion may be inaccurate. Consider using '#align polynomial.card_roots_le_map_of_injective Polynomial.card_roots_le_map_of_injectiveₓ'. -/
 theorem card_roots_le_map_of_injective [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B}
     (hf : Function.Injective f) : p.roots.card ≤ (p.map f).roots.card :=
@@ -1877,7 +1877,7 @@ theorem card_roots_le_map_of_injective [IsDomain A] [IsDomain B] {p : A[X]} {f :
 lean 3 declaration is
   forall {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommRing.{u1} A] [_inst_2 : CommRing.{u2} B] [_inst_3 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))] [_inst_4 : IsDomain.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))] {p : Polynomial.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))} {f : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))}, (Function.Injective.{succ u1, succ u2} A B (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f)) -> (Eq.{1} Nat (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} A) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} A) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} A) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} A) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} A) (Multiset.orderedCancelAddCommMonoid.{u1} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} A) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} A) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} A) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} A) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} A) (Multiset.orderedCancelAddCommMonoid.{u1} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} A) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} A) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} A) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} A) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} A) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} A) (Multiset.orderedCancelAddCommMonoid.{u1} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} A) (Polynomial.roots.{u1} A _inst_1 _inst_3 p)) (Polynomial.natDegree.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) p)) -> (Eq.{succ u2} (Multiset.{u2} B) (Multiset.map.{u1, u2} A B (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f) (Polynomial.roots.{u1} A _inst_1 _inst_3 p)) (Polynomial.roots.{u2} B _inst_2 _inst_4 (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p)))
 but is expected to have type
-  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))] [_inst_4 : IsDomain.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))] {p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))} {f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f)) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} A) => Nat) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) (fun (_x : Multiset.{u2} A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} A) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} A) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} A) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (Polynomial.natDegree.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) p)) -> (Eq.{succ u1} (Multiset.{u1} B) (Multiset.map.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (Polynomial.roots.{u1} B _inst_2 _inst_4 (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p)))
+  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))] [_inst_4 : IsDomain.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))] {p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))} {f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f)) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} A) => Nat) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) (fun (_x : Multiset.{u2} A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} A) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} A) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} A) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (Polynomial.natDegree.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) p)) -> (Eq.{succ u1} (Multiset.{u1} B) (Multiset.map.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (Polynomial.roots.{u1} B _inst_2 _inst_4 (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_map_of_injective_of_card_eq_nat_degree Polynomial.roots_map_of_injective_of_card_eq_natDegreeₓ'. -/
 theorem roots_map_of_injective_of_card_eq_natDegree [IsDomain A] [IsDomain B] {p : A[X]}
     {f : A →+* B} (hf : Function.Injective f) (hroots : p.roots.card = p.natDegree) :

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

@@ -1083,7 +1083,7 @@ theorem roots_C_mul_X_pow (ha : a ≠ 0) (n : ℕ) : (C a * X ^ n).roots = n •
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{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 (CommRing.toRing.{u1} R _inst_1)))))))))) -> (forall (n : Nat), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (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)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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)))))) (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)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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)))))) (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))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (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} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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)))))) (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.monomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) n) a)) (SMul.smul.{0, u1} Nat (Multiset.{u1} R) (AddMonoid.SMul.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) n (Singleton.singleton.{u1, u1} R (Multiset.{u1} R) (Multiset.hasSingleton.{u1} R) (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 (CommRing.toRing.{u1} R _inst_1))))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))], (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))) -> (forall (n : Nat), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (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)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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)))))) (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))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (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} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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)))))) (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.monomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) n) a)) (HSMul.hSMul.{0, u1, u1} Nat (Multiset.{u1} R) (Multiset.{u1} R) (instHSMul.{0, u1} Nat (Multiset.{u1} R) (AddMonoid.SMul.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) n (Singleton.singleton.{u1, u1} R (Multiset.{u1} R) (Multiset.instSingletonMultiset.{u1} R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))))))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))], (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))) -> (forall (n : Nat), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (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)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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)))))) (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))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (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} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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)))))) (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.monomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) n) a)) (HSMul.hSMul.{0, u1, u1} Nat (Multiset.{u1} R) (Multiset.{u1} R) (instHSMul.{0, u1} Nat (Multiset.{u1} R) (AddMonoid.SMul.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) n (Singleton.singleton.{u1, u1} R (Multiset.{u1} R) (Multiset.instSingletonMultiset.{u1} R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_monomial Polynomial.roots_monomialₓ'. -/
 @[simp]
 theorem roots_monomial (ha : a ≠ 0) (n : ℕ) : (monomial n a).roots = n • {0} := by

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

@@ -199,7 +199,7 @@ theorem natDegree_pow (p : R[X]) (n : ℕ) : natDegree (p ^ n) = n * natDegree p
 
 /- warning: polynomial.degree_le_mul_left -> Polynomial.degree_le_mul_left is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {q : Polynomial.{u1} R _inst_1} (p : Polynomial.{u1} R _inst_1), (Ne.{succ u1} (Polynomial.{u1} R _inst_1) q (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R _inst_1 p) (Polynomial.degree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p q)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {q : Polynomial.{u1} R _inst_1} (p : Polynomial.{u1} R _inst_1), (Ne.{succ u1} (Polynomial.{u1} R _inst_1) q (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toHasLe.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R _inst_1 p) (Polynomial.degree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p q)))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))] {q : Polynomial.{u1} R _inst_1} (p : Polynomial.{u1} R _inst_1), (Ne.{succ u1} (Polynomial.{u1} R _inst_1) q (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R _inst_1 p) (Polynomial.degree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p q)))
 Case conversion may be inaccurate. Consider using '#align polynomial.degree_le_mul_left Polynomial.degree_le_mul_leftₓ'. -/
@@ -224,7 +224,7 @@ theorem natDegree_le_of_dvd {p q : R[X]} (h1 : p ∣ q) (h2 : q ≠ 0) : p.natDe
 
 /- warning: polynomial.degree_le_of_dvd -> Polynomial.degree_le_of_dvd is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, (Dvd.Dvd.{u1} (Polynomial.{u1} R _inst_1) (semigroupDvd.{u1} (Polynomial.{u1} R _inst_1) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R _inst_1) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) p q) -> (Ne.{succ u1} (Polynomial.{u1} R _inst_1) q (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R _inst_1 p) (Polynomial.degree.{u1} R _inst_1 q))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, (Dvd.Dvd.{u1} (Polynomial.{u1} R _inst_1) (semigroupDvd.{u1} (Polynomial.{u1} R _inst_1) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R _inst_1) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) p q) -> (Ne.{succ u1} (Polynomial.{u1} R _inst_1) q (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toHasLe.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R _inst_1 p) (Polynomial.degree.{u1} R _inst_1 q))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, (Dvd.dvd.{u1} (Polynomial.{u1} R _inst_1) (semigroupDvd.{u1} (Polynomial.{u1} R _inst_1) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R _inst_1) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) p q) -> (Ne.{succ u1} (Polynomial.{u1} R _inst_1) q (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R _inst_1 p) (Polynomial.degree.{u1} R _inst_1 q))
 Case conversion may be inaccurate. Consider using '#align polynomial.degree_le_of_dvd Polynomial.degree_le_of_dvdₓ'. -/
@@ -236,7 +236,7 @@ theorem degree_le_of_dvd {p q : R[X]} (h1 : p ∣ q) (h2 : q ≠ 0) : degree p 
 
 /- warning: polynomial.eq_zero_of_dvd_of_degree_lt -> Polynomial.eq_zero_of_dvd_of_degree_lt is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, (Dvd.Dvd.{u1} (Polynomial.{u1} R _inst_1) (semigroupDvd.{u1} (Polynomial.{u1} R _inst_1) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R _inst_1) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) p q) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R _inst_1 q) (Polynomial.degree.{u1} R _inst_1 p)) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) q (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, (Dvd.Dvd.{u1} (Polynomial.{u1} R _inst_1) (semigroupDvd.{u1} (Polynomial.{u1} R _inst_1) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R _inst_1) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) p q) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R _inst_1 q) (Polynomial.degree.{u1} R _inst_1 p)) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) q (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, (Dvd.dvd.{u1} (Polynomial.{u1} R _inst_1) (semigroupDvd.{u1} (Polynomial.{u1} R _inst_1) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R _inst_1) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) p q) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R _inst_1 q) (Polynomial.degree.{u1} R _inst_1 p)) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) q (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_zero_of_dvd_of_degree_lt Polynomial.eq_zero_of_dvd_of_degree_ltₓ'. -/
@@ -260,7 +260,7 @@ theorem eq_zero_of_dvd_of_natDegree_lt {p q : R[X]} (h₁ : p ∣ q) (h₂ : nat
 
 /- warning: polynomial.not_dvd_of_degree_lt -> Polynomial.not_dvd_of_degree_lt is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} (Polynomial.{u1} R _inst_1) q (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R _inst_1 q) (Polynomial.degree.{u1} R _inst_1 p)) -> (Not (Dvd.Dvd.{u1} (Polynomial.{u1} R _inst_1) (semigroupDvd.{u1} (Polynomial.{u1} R _inst_1) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R _inst_1) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) p q))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} (Polynomial.{u1} R _inst_1) q (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R _inst_1 q) (Polynomial.degree.{u1} R _inst_1 p)) -> (Not (Dvd.Dvd.{u1} (Polynomial.{u1} R _inst_1) (semigroupDvd.{u1} (Polynomial.{u1} R _inst_1) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R _inst_1) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) p q))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} (Polynomial.{u1} R _inst_1) q (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R _inst_1 q) (Polynomial.degree.{u1} R _inst_1 p)) -> (Not (Dvd.dvd.{u1} (Polynomial.{u1} R _inst_1) (semigroupDvd.{u1} (Polynomial.{u1} R _inst_1) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R _inst_1) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) p q))
 Case conversion may be inaccurate. Consider using '#align polynomial.not_dvd_of_degree_lt Polynomial.not_dvd_of_degree_ltₓ'. -/
@@ -703,7 +703,7 @@ theorem rootMultiplicity_X_sub_C_pow (a : R) (n : ℕ) : rootMultiplicity a ((X
 
 /- warning: polynomial.exists_multiset_roots -> Polynomial.exists_multiset_roots 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (Exists.{succ u1} (Multiset.{u1} R) (fun (s : Multiset.{u1} R) => And (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s)) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) (forall (a : R), Eq.{1} Nat (Multiset.count.{u1} R (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)) a s) (Polynomial.rootMultiplicity.{u1} R _inst_1 a 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (Exists.{succ u1} (Multiset.{u1} R) (fun (s : Multiset.{u1} R) => And (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))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s)) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) (forall (a : R), Eq.{1} Nat (Multiset.count.{u1} R (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)) a s) (Polynomial.rootMultiplicity.{u1} R _inst_1 a 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))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) -> (Exists.{succ u1} (Multiset.{u1} R) (fun (s : Multiset.{u1} R) => And (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s)) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) (forall (a : R), Eq.{1} Nat (Multiset.count.{u1} R (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)) a s) (Polynomial.rootMultiplicity.{u1} R _inst_1 a p))))
 Case conversion may be inaccurate. Consider using '#align polynomial.exists_multiset_roots Polynomial.exists_multiset_rootsₓ'. -/
@@ -766,7 +766,7 @@ theorem roots_zero : (0 : R[X]).roots = 0 :=
 
 /- warning: polynomial.card_roots -> Polynomial.card_roots 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))) (Polynomial.degree.{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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{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))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))) (Polynomial.degree.{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))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.card_roots Polynomial.card_rootsₓ'. -/
@@ -792,7 +792,7 @@ theorem card_roots' (p : R[X]) : p.roots.card ≤ natDegree p :=
 
 /- warning: polynomial.card_roots_sub_C -> Polynomial.card_roots_sub_C 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {a : R}, (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 (CommRing.toRing.{u1} R _inst_1)) p)) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a))))) (Polynomial.degree.{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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {a : R}, (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 (CommRing.toRing.{u1} R _inst_1)) p)) -> (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))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a))))) (Polynomial.degree.{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))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {a : R}, (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 (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a))))) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.card_roots_sub_C Polynomial.card_roots_sub_Cₓ'. -/
@@ -807,7 +807,7 @@ theorem card_roots_sub_C {p : R[X]} {a : R} (hp0 : 0 < degree p) :
 
 /- warning: polynomial.card_roots_sub_C' -> Polynomial.card_roots_sub_C' 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {a : R}, (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 (CommRing.toRing.{u1} R _inst_1)) p)) -> (LE.le.{0} Nat Nat.hasLe (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a)))) (Polynomial.natDegree.{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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {a : R}, (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 (CommRing.toRing.{u1} R _inst_1)) p)) -> (LE.le.{0} Nat Nat.hasLe (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a)))) (Polynomial.natDegree.{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))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {a : R}, (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 (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) -> (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a)))) instLENat (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) 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(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))) a)))) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.card_roots_sub_C' Polynomial.card_roots_sub_C'ₓ'. -/
@@ -873,17 +873,25 @@ theorem eq_zero_of_infinite_isRoot (p : R[X]) (h : Set.Infinite { x | IsRoot p x
 #align polynomial.eq_zero_of_infinite_is_root Polynomial.eq_zero_of_infinite_isRoot
 -/
 
-#print Polynomial.exists_max_root /-
+/- warning: polynomial.exists_max_root -> Polynomial.exists_max_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 : LinearOrder.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (Exists.{succ u1} R (fun (x₀ : R) => forall (x : R), (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p x) -> (LE.le.{u1} R (Preorder.toHasLe.{u1} R (PartialOrder.toPreorder.{u1} R (SemilatticeInf.toPartialOrder.{u1} R (Lattice.toSemilatticeInf.{u1} R (LinearOrder.toLattice.{u1} R _inst_3))))) x x₀)))
+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 : LinearOrder.{u1} R] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) -> (Exists.{succ u1} R (fun (x₀ : R) => forall (x : R), (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p x) -> (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (SemilatticeInf.toPartialOrder.{u1} R (Lattice.toSemilatticeInf.{u1} R (DistribLattice.toLattice.{u1} R (instDistribLattice.{u1} R _inst_3)))))) x x₀)))
+Case conversion may be inaccurate. Consider using '#align polynomial.exists_max_root Polynomial.exists_max_rootₓ'. -/
 theorem exists_max_root [LinearOrder R] (p : R[X]) (hp : p ≠ 0) : ∃ x₀, ∀ x, p.IsRoot x → x ≤ x₀ :=
   Set.exists_upper_bound_image _ _ <| finite_setOf_isRoot hp
 #align polynomial.exists_max_root Polynomial.exists_max_root
--/
 
-#print Polynomial.exists_min_root /-
+/- warning: polynomial.exists_min_root -> Polynomial.exists_min_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 : LinearOrder.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (Exists.{succ u1} R (fun (x₀ : R) => forall (x : R), (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p x) -> (LE.le.{u1} R (Preorder.toHasLe.{u1} R (PartialOrder.toPreorder.{u1} R (SemilatticeInf.toPartialOrder.{u1} R (Lattice.toSemilatticeInf.{u1} R (LinearOrder.toLattice.{u1} R _inst_3))))) x₀ x)))
+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 : LinearOrder.{u1} R] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) -> (Exists.{succ u1} R (fun (x₀ : R) => forall (x : R), (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p x) -> (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (SemilatticeInf.toPartialOrder.{u1} R (Lattice.toSemilatticeInf.{u1} R (DistribLattice.toLattice.{u1} R (instDistribLattice.{u1} R _inst_3)))))) x₀ x)))
+Case conversion may be inaccurate. Consider using '#align polynomial.exists_min_root Polynomial.exists_min_rootₓ'. -/
 theorem exists_min_root [LinearOrder R] (p : R[X]) (hp : p ≠ 0) : ∃ x₀, ∀ x, p.IsRoot x → x₀ ≤ x :=
   Set.exists_lower_bound_image _ _ <| finite_setOf_isRoot hp
 #align polynomial.exists_min_root Polynomial.exists_min_root
--/
 
 #print Polynomial.eq_of_infinite_eval_eq /-
 theorem eq_of_infinite_eval_eq (p q : R[X]) (h : Set.Infinite { x | eval x p = eval x q }) :
@@ -903,7 +911,7 @@ theorem roots_mul {p q : R[X]} (hpq : p * q ≠ 0) : (p * q).roots = p.roots + q
 
 /- warning: polynomial.roots.le_of_dvd -> Polynomial.roots.le_of_dvd 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) q (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) p q) -> (LE.le.{u1} (Multiset.{u1} R) (Preorder.toLE.{u1} (Multiset.{u1} R) (PartialOrder.toPreorder.{u1} (Multiset.{u1} R) (Multiset.partialOrder.{u1} R))) (Polynomial.roots.{u1} R _inst_1 _inst_2 p) (Polynomial.roots.{u1} R _inst_1 _inst_2 q))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) q (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) p q) -> (LE.le.{u1} (Multiset.{u1} R) (Preorder.toHasLe.{u1} (Multiset.{u1} R) (PartialOrder.toPreorder.{u1} (Multiset.{u1} R) (Multiset.partialOrder.{u1} R))) (Polynomial.roots.{u1} R _inst_1 _inst_2 p) (Polynomial.roots.{u1} R _inst_1 _inst_2 q))
 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))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) q (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) -> (Dvd.dvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) p q) -> (LE.le.{u1} (Multiset.{u1} R) (Preorder.toLE.{u1} (Multiset.{u1} R) (PartialOrder.toPreorder.{u1} (Multiset.{u1} R) (Multiset.instPartialOrderMultiset.{u1} R))) (Polynomial.roots.{u1} R _inst_1 _inst_2 p) (Polynomial.roots.{u1} R _inst_1 _inst_2 q))
 Case conversion may be inaccurate. Consider using '#align polynomial.roots.le_of_dvd Polynomial.roots.le_of_dvdₓ'. -/
@@ -925,7 +933,7 @@ theorem mem_roots_sub_C' {p : R[X]} {a x : R} : x ∈ (p - C a).roots ↔ p ≠
 
 /- warning: polynomial.mem_roots_sub_C -> Polynomial.mem_roots_sub_C 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {a : R} {x : R}, (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 (CommRing.toRing.{u1} R _inst_1)) p)) -> (Iff (Membership.Mem.{u1, u1} R (Multiset.{u1} R) (Multiset.hasMem.{u1} R) x (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a)))) (Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x p) a))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {a : R} {x : R}, (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 (CommRing.toRing.{u1} R _inst_1)) p)) -> (Iff (Membership.Mem.{u1, u1} R (Multiset.{u1} R) (Multiset.hasMem.{u1} R) x (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a)))) (Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x p) a))
 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))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {a : R} {x : R}, (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 (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) -> (Iff (Membership.mem.{u1, u1} R (Multiset.{u1} R) (Multiset.instMembershipMultiset.{u1} R) x (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R 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(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))) a)))) (Eq.{succ u1} R (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) x p) a))
 Case conversion may be inaccurate. Consider using '#align polynomial.mem_roots_sub_C Polynomial.mem_roots_sub_Cₓ'. -/
@@ -1536,7 +1544,12 @@ theorem degree_eq_one_of_irreducible_of_root (hi : Irreducible p) {x : R} (hx :
     fun hgu => by rw [hg, degree_mul, degree_X_sub_C, degree_eq_zero_of_is_unit hgu, add_zero]
 #align polynomial.degree_eq_one_of_irreducible_of_root Polynomial.degree_eq_one_of_irreducible_of_root
 
-#print Polynomial.leadingCoeff_divByMonic_of_monic /-
+/- warning: polynomial.leading_coeff_div_by_monic_of_monic -> Polynomial.leadingCoeff_divByMonic_of_monic is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) q) -> (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 (CommRing.toRing.{u1} R _inst_3)) q) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) p)) -> (Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) (Polynomial.divByMonic.{u1} R (CommRing.toRing.{u1} R _inst_3) p q)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) p))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))}, (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) q) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) q) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) p)) -> (Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) (Polynomial.divByMonic.{u1} R (CommRing.toRing.{u1} R _inst_3) p q)) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) p))
+Case conversion may be inaccurate. Consider using '#align polynomial.leading_coeff_div_by_monic_of_monic Polynomial.leadingCoeff_divByMonic_of_monicₓ'. -/
 /-- Division by a monic polynomial doesn't change the leading coefficient. -/
 theorem leadingCoeff_divByMonic_of_monic {R : Type u} [CommRing R] {p q : R[X]} (hmonic : q.Monic)
     (hdegree : q.degree ≤ p.degree) : (p /ₘ q).leadingCoeff = p.leadingCoeff :=
@@ -1550,7 +1563,6 @@ theorem leadingCoeff_divByMonic_of_monic {R : Type u} [CommRing R] {p q : R[X]}
   rw [degree_mul' h, degree_add_div_by_monic hmonic hdegree]
   exact (degree_mod_by_monic_lt p hmonic).trans_le hdegree
 #align polynomial.leading_coeff_div_by_monic_of_monic Polynomial.leadingCoeff_divByMonic_of_monic
--/
 
 /- warning: polynomial.leading_coeff_div_by_monic_X_sub_C -> Polynomial.leadingCoeff_divByMonic_X_sub_C is a dubious translation:
 lean 3 declaration is
@@ -1666,7 +1678,7 @@ theorem prod_multiset_X_sub_C_dvd (p : R[X]) : (p.roots.map fun a => X - C a).Pr
 
 /- warning: multiset.prod_X_sub_C_dvd_iff_le_roots -> Multiset.prod_X_sub_C_dvd_iff_le_roots 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (forall (s : Multiset.{u1} R), Iff (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) s)) p) (LE.le.{u1} (Multiset.{u1} R) (Preorder.toLE.{u1} (Multiset.{u1} R) (PartialOrder.toPreorder.{u1} (Multiset.{u1} R) (Multiset.partialOrder.{u1} R))) s (Polynomial.roots.{u1} R _inst_1 _inst_2 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (forall (s : Multiset.{u1} R), Iff (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) s)) p) (LE.le.{u1} (Multiset.{u1} R) (Preorder.toHasLe.{u1} (Multiset.{u1} R) (PartialOrder.toPreorder.{u1} (Multiset.{u1} R) (Multiset.partialOrder.{u1} R))) s (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))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) -> (forall (s : Multiset.{u1} R), Iff (Dvd.dvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) s)) p) (LE.le.{u1} (Multiset.{u1} R) (Preorder.toLE.{u1} (Multiset.{u1} R) (PartialOrder.toPreorder.{u1} (Multiset.{u1} R) (Multiset.instPartialOrderMultiset.{u1} R))) s (Polynomial.roots.{u1} R _inst_1 _inst_2 p)))
 Case conversion may be inaccurate. Consider using '#align multiset.prod_X_sub_C_dvd_iff_le_roots Multiset.prod_X_sub_C_dvd_iff_le_rootsₓ'. -/
@@ -1811,7 +1823,7 @@ theorem count_map_roots_of_injective [IsDomain A] (p : A[X]) {f : A →+* B}
 
 /- warning: polynomial.map_roots_le -> Polynomial.map_roots_le is a dubious translation:
 lean 3 declaration is
-  forall {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommRing.{u1} A] [_inst_2 : CommRing.{u2} B] [_inst_3 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))] [_inst_4 : IsDomain.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))] {p : Polynomial.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))} {f : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))}, (Ne.{succ u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p) (OfNat.ofNat.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) 0 (OfNat.mk.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) 0 (Zero.zero.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) (Polynomial.zero.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))))))) -> (LE.le.{u2} (Multiset.{u2} B) (Preorder.toLE.{u2} (Multiset.{u2} B) (PartialOrder.toPreorder.{u2} (Multiset.{u2} B) (Multiset.partialOrder.{u2} B))) (Multiset.map.{u1, u2} A B (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f) (Polynomial.roots.{u1} A _inst_1 _inst_3 p)) (Polynomial.roots.{u2} B _inst_2 _inst_4 (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p)))
+  forall {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommRing.{u1} A] [_inst_2 : CommRing.{u2} B] [_inst_3 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))] [_inst_4 : IsDomain.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))] {p : Polynomial.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))} {f : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))}, (Ne.{succ u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p) (OfNat.ofNat.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) 0 (OfNat.mk.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) 0 (Zero.zero.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) (Polynomial.zero.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))))))) -> (LE.le.{u2} (Multiset.{u2} B) (Preorder.toHasLe.{u2} (Multiset.{u2} B) (PartialOrder.toPreorder.{u2} (Multiset.{u2} B) (Multiset.partialOrder.{u2} B))) (Multiset.map.{u1, u2} A B (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f) (Polynomial.roots.{u1} A _inst_1 _inst_3 p)) (Polynomial.roots.{u2} B _inst_2 _inst_4 (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p)))
 but is expected to have type
   forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))] [_inst_4 : IsDomain.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))] {p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))} {f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))}, (Ne.{succ u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p) (OfNat.ofNat.{u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (Polynomial.zero.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))))) -> (LE.le.{u1} (Multiset.{u1} B) (Preorder.toLE.{u1} (Multiset.{u1} B) (PartialOrder.toPreorder.{u1} (Multiset.{u1} B) (Multiset.instPartialOrderMultiset.{u1} B))) (Multiset.map.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (Polynomial.roots.{u1} B _inst_2 _inst_4 (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_roots_le Polynomial.map_roots_leₓ'. -/
@@ -1824,7 +1836,7 @@ theorem map_roots_le [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (h : p
 
 /- warning: polynomial.map_roots_le_of_injective -> Polynomial.map_roots_le_of_injective is a dubious translation:
 lean 3 declaration is
-  forall {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommRing.{u1} A] [_inst_2 : CommRing.{u2} B] [_inst_3 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))] [_inst_4 : IsDomain.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))] (p : Polynomial.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))) {f : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))}, (Function.Injective.{succ u1, succ u2} A B (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f)) -> (LE.le.{u2} (Multiset.{u2} B) (Preorder.toLE.{u2} (Multiset.{u2} B) (PartialOrder.toPreorder.{u2} (Multiset.{u2} B) (Multiset.partialOrder.{u2} B))) (Multiset.map.{u1, u2} A B (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f) (Polynomial.roots.{u1} A _inst_1 _inst_3 p)) (Polynomial.roots.{u2} B _inst_2 _inst_4 (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p)))
+  forall {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommRing.{u1} A] [_inst_2 : CommRing.{u2} B] [_inst_3 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))] [_inst_4 : IsDomain.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))] (p : Polynomial.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))) {f : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))}, (Function.Injective.{succ u1, succ u2} A B (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f)) -> (LE.le.{u2} (Multiset.{u2} B) (Preorder.toHasLe.{u2} (Multiset.{u2} B) (PartialOrder.toPreorder.{u2} (Multiset.{u2} B) (Multiset.partialOrder.{u2} B))) (Multiset.map.{u1, u2} A B (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f) (Polynomial.roots.{u1} A _inst_1 _inst_3 p)) (Polynomial.roots.{u2} B _inst_2 _inst_4 (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p)))
 but is expected to have type
   forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))] [_inst_4 : IsDomain.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))] (p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) {f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f)) -> (LE.le.{u1} (Multiset.{u1} B) (Preorder.toLE.{u1} (Multiset.{u1} B) (PartialOrder.toPreorder.{u1} (Multiset.{u1} B) (Multiset.instPartialOrderMultiset.{u1} B))) (Multiset.map.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (Polynomial.roots.{u1} B _inst_2 _inst_4 (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_roots_le_of_injective Polynomial.map_roots_le_of_injectiveₓ'. -/

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

@@ -1390,9 +1390,9 @@ theorem rootSet_finite (p : T[X]) (S : Type _) [CommRing S] [IsDomain S] [Algebr
 
 /- warning: polynomial.bUnion_roots_finite -> Polynomial.bUnion_roots_finite is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_4 : Semiring.{u1} R] [_inst_5 : CommRing.{u2} S] [_inst_6 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5))] (m : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_4) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))) (d : Nat) {U : Set.{u1} R}, (Set.Finite.{u1} R U) -> (Set.Finite.{u2} S (Set.unionᵢ.{u2, succ u1} S (Polynomial.{u1} R _inst_4) (fun (f : Polynomial.{u1} R _inst_4) => Set.unionᵢ.{u2, 0} S (And (LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R _inst_4 f) d) (forall (i : Nat), Membership.Mem.{u1, u1} R (Set.{u1} R) (Set.hasMem.{u1} R) (Polynomial.coeff.{u1} R _inst_4 f i) U)) (fun (hf : And (LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R _inst_4 f) d) (forall (i : Nat), Membership.Mem.{u1, u1} R (Set.{u1} R) (Set.hasMem.{u1} R) (Polynomial.coeff.{u1} R _inst_4 f i) U)) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} S) (Set.{u2} S) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} S) (Set.{u2} S) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} S) (Set.{u2} S) (Finset.Set.hasCoeT.{u2} S))) (Multiset.toFinset.{u2} S (fun (a : S) (b : S) => Classical.propDecidable (Eq.{succ u2} S a b)) (Polynomial.roots.{u2} S _inst_5 _inst_6 (Polynomial.map.{u1, u2} R S _inst_4 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5)) m f)))))))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_4 : Semiring.{u1} R] [_inst_5 : CommRing.{u2} S] [_inst_6 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5))] (m : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_4) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))) (d : Nat) {U : Set.{u1} R}, (Set.Finite.{u1} R U) -> (Set.Finite.{u2} S (Set.iUnion.{u2, succ u1} S (Polynomial.{u1} R _inst_4) (fun (f : Polynomial.{u1} R _inst_4) => Set.iUnion.{u2, 0} S (And (LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R _inst_4 f) d) (forall (i : Nat), Membership.Mem.{u1, u1} R (Set.{u1} R) (Set.hasMem.{u1} R) (Polynomial.coeff.{u1} R _inst_4 f i) U)) (fun (hf : And (LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R _inst_4 f) d) (forall (i : Nat), Membership.Mem.{u1, u1} R (Set.{u1} R) (Set.hasMem.{u1} R) (Polynomial.coeff.{u1} R _inst_4 f i) U)) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} S) (Set.{u2} S) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} S) (Set.{u2} S) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} S) (Set.{u2} S) (Finset.Set.hasCoeT.{u2} S))) (Multiset.toFinset.{u2} S (fun (a : S) (b : S) => Classical.propDecidable (Eq.{succ u2} S a b)) (Polynomial.roots.{u2} S _inst_5 _inst_6 (Polynomial.map.{u1, u2} R S _inst_4 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5)) m f)))))))
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_4 : Semiring.{u2} R] [_inst_5 : CommRing.{u1} S] [_inst_6 : IsDomain.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))] (m : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_4) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (d : Nat) {U : Set.{u2} R}, (Set.Finite.{u2} R U) -> (Set.Finite.{u1} S (Set.unionᵢ.{u1, succ u2} S (Polynomial.{u2} R _inst_4) (fun (f : Polynomial.{u2} R _inst_4) => Set.unionᵢ.{u1, 0} S (And (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u2} R _inst_4 f) d) (forall (i : Nat), Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) (Polynomial.coeff.{u2} R _inst_4 f i) U)) (fun (hf : And (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u2} R _inst_4 f) d) (forall (i : Nat), Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) (Polynomial.coeff.{u2} R _inst_4 f i) U)) => Finset.toSet.{u1} S (Multiset.toFinset.{u1} S (fun (a : S) (b : S) => Classical.propDecidable (Eq.{succ u1} S a b)) (Polynomial.roots.{u1} S _inst_5 _inst_6 (Polynomial.map.{u2, u1} R S _inst_4 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)) m f)))))))
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_4 : Semiring.{u2} R] [_inst_5 : CommRing.{u1} S] [_inst_6 : IsDomain.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))] (m : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_4) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (d : Nat) {U : Set.{u2} R}, (Set.Finite.{u2} R U) -> (Set.Finite.{u1} S (Set.iUnion.{u1, succ u2} S (Polynomial.{u2} R _inst_4) (fun (f : Polynomial.{u2} R _inst_4) => Set.iUnion.{u1, 0} S (And (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u2} R _inst_4 f) d) (forall (i : Nat), Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) (Polynomial.coeff.{u2} R _inst_4 f i) U)) (fun (hf : And (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u2} R _inst_4 f) d) (forall (i : Nat), Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) (Polynomial.coeff.{u2} R _inst_4 f i) U)) => Finset.toSet.{u1} S (Multiset.toFinset.{u1} S (fun (a : S) (b : S) => Classical.propDecidable (Eq.{succ u1} S a b)) (Polynomial.roots.{u1} S _inst_5 _inst_6 (Polynomial.map.{u2, u1} R S _inst_4 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)) m f)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.bUnion_roots_finite Polynomial.bUnion_roots_finiteₓ'. -/
 /-- The set of roots of all polynomials of bounded degree and having coefficients in a finite set
 is finite. -/
@@ -1400,7 +1400,7 @@ theorem bUnion_roots_finite {R S : Type _} [Semiring R] [CommRing S] [IsDomain S
     (d : ℕ) {U : Set R} (h : U.Finite) :
     (⋃ (f : R[X]) (hf : f.natDegree ≤ d ∧ ∀ i, f.coeff i ∈ U),
         ((f.map m).roots.toFinset : Set S)).Finite :=
-  Set.Finite.bunionᵢ
+  Set.Finite.biUnion
     (by
       -- We prove that the set of polynomials under consideration is finite because its
       -- image by the injective map `π` is finite

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

@@ -515,7 +515,7 @@ variable [CommRing R]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (forall {a : R} {n : Nat}, Iff (LE.le.{0} Nat Nat.hasLe n (Polynomial.rootMultiplicity.{u1} R _inst_1 a p)) (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) n) p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) -> (forall {a : R} {n : Nat}, Iff (LE.le.{0} Nat instLENat n (Polynomial.rootMultiplicity.{u1} R _inst_1 a p)) (Dvd.dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) n) p))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) -> (forall {a : R} {n : Nat}, Iff (LE.le.{0} Nat instLENat n (Polynomial.rootMultiplicity.{u1} R _inst_1 a p)) (Dvd.dvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) n) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.le_root_multiplicity_iff Polynomial.le_rootMultiplicity_iffₓ'. -/
 /-- The multiplicity of `a` as root of a nonzero polynomial `p` is at least `n` iff
   `(X - a) ^ n` divides `p`. -/
@@ -533,7 +533,7 @@ theorem le_rootMultiplicity_iff {p : R[X]} (p0 : p ≠ 0) {a : R} {n : ℕ} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (forall (a : R) (n : Nat), Iff (LE.le.{0} Nat Nat.hasLe (Polynomial.rootMultiplicity.{u1} R _inst_1 a p) n) (Not (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) p)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) -> (forall (a : R) (n : Nat), Iff (LE.le.{0} Nat instLENat (Polynomial.rootMultiplicity.{u1} R _inst_1 a p) n) (Not (Dvd.dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p)))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) -> (forall (a : R) (n : Nat), Iff (LE.le.{0} Nat instLENat (Polynomial.rootMultiplicity.{u1} R _inst_1 a p) n) (Not (Dvd.dvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.root_multiplicity_le_iff Polynomial.rootMultiplicity_le_iffₓ'. -/
 theorem rootMultiplicity_le_iff {p : R[X]} (p0 : p ≠ 0) (a : R) (n : ℕ) :
     rootMultiplicity a p ≤ n ↔ ¬(X - C a) ^ (n + 1) ∣ p := by
@@ -544,7 +544,7 @@ theorem rootMultiplicity_le_iff {p : R[X]} (p0 : p ≠ 0) (a : R) (n : ℕ) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (forall (a : R), Not (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Polynomial.rootMultiplicity.{u1} R _inst_1 a p) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) -> (forall (a : R), Not (Dvd.dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Polynomial.rootMultiplicity.{u1} R _inst_1 a p) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) -> (forall (a : R), Not (Dvd.dvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Polynomial.rootMultiplicity.{u1} R _inst_1 a p) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.pow_root_multiplicity_not_dvd Polynomial.pow_rootMultiplicity_not_dvdₓ'. -/
 theorem pow_rootMultiplicity_not_dvd {p : R[X]} (p0 : p ≠ 0) (a : R) :
     ¬(X - C a) ^ (rootMultiplicity a p + 1) ∣ p := by rw [← root_multiplicity_le_iff p0]
@@ -554,7 +554,7 @@ theorem pow_rootMultiplicity_not_dvd {p : R[X]} (p0 : p ≠ 0) (a : R) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} (a : R), (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HAdd.hAdd.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p q) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (LE.le.{0} Nat Nat.hasLe (LinearOrder.min.{0} Nat Nat.linearOrder (Polynomial.rootMultiplicity.{u1} R _inst_1 a p) (Polynomial.rootMultiplicity.{u1} R _inst_1 a q)) (Polynomial.rootMultiplicity.{u1} R _inst_1 a (HAdd.hAdd.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p q)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} (a : R), (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HAdd.hAdd.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p q) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) -> (LE.le.{0} Nat instLENat (Min.min.{0} Nat instMinNat (Polynomial.rootMultiplicity.{u1} R _inst_1 a p) (Polynomial.rootMultiplicity.{u1} R _inst_1 a q)) (Polynomial.rootMultiplicity.{u1} R _inst_1 a (HAdd.hAdd.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p q)))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} (a : R), (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (HAdd.hAdd.{u1, 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))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) p q) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) -> (LE.le.{0} Nat instLENat (Min.min.{0} Nat instMinNat (Polynomial.rootMultiplicity.{u1} R _inst_1 a p) (Polynomial.rootMultiplicity.{u1} R _inst_1 a q)) (Polynomial.rootMultiplicity.{u1} R _inst_1 a (HAdd.hAdd.{u1, 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))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) p q)))
 Case conversion may be inaccurate. Consider using '#align polynomial.root_multiplicity_add Polynomial.rootMultiplicity_addₓ'. -/
 /-- The multiplicity of `p + q` is at least the minimum of the multiplicities. -/
 theorem rootMultiplicity_add {p q : R[X]} (a : R) (hzero : p + q ≠ 0) :
@@ -576,7 +576,7 @@ open Multiset
 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))] (r : R), Prime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) r))
 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))] (r : R), Prime.{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))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{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))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) r))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (r : R), Prime.{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))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{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))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) r))
 Case conversion may be inaccurate. Consider using '#align polynomial.prime_X_sub_C Polynomial.prime_X_sub_Cₓ'. -/
 theorem prime_X_sub_C (r : R) : Prime (X - C r) :=
   ⟨X_sub_C_ne_zero r, not_isUnit_X_sub_C r, fun _ _ =>
@@ -604,7 +604,7 @@ theorem Monic.prime_of_degree_eq_one (hp1 : degree p = 1) (hm : Monic p) : Prime
 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))] (r : R), Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) r))
 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))] (r : R), Irreducible.{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))) (Semiring.toMonoidWithZero.{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))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{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))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) r))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (r : R), Irreducible.{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))) (Semiring.toMonoidWithZero.{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))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{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))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) r))
 Case conversion may be inaccurate. Consider using '#align polynomial.irreducible_X_sub_C Polynomial.irreducible_X_sub_Cₓ'. -/
 theorem irreducible_X_sub_C (r : R) : Irreducible (X - C r) :=
   (prime_X_sub_C r).Irreducible
@@ -614,7 +614,7 @@ theorem irreducible_X_sub_C (r : R) : Irreducible (X - C 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))], Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))
 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))], Irreducible.{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))) (Semiring.toMonoidWithZero.{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.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_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))], Irreducible.{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))) (Semiring.toMonoidWithZero.{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.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))
 Case conversion may be inaccurate. Consider using '#align polynomial.irreducible_X Polynomial.irreducible_Xₓ'. -/
 theorem irreducible_X : Irreducible (X : R[X]) :=
   Prime.irreducible prime_X
@@ -624,7 +624,7 @@ theorem irreducible_X : Irreducible (X : 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{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))))) -> (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) -> (Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) (OfNat.ofNat.{0} (WithBot.{0} Nat) 1 (One.toOfNat1.{0} (WithBot.{0} Nat) (WithBot.one.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) -> (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) -> (Irreducible.{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))) (Semiring.toMonoidWithZero.{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))))) 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))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p) (OfNat.ofNat.{0} (WithBot.{0} Nat) 1 (One.toOfNat1.{0} (WithBot.{0} Nat) (WithBot.one.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) -> (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p) -> (Irreducible.{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))) (Semiring.toMonoidWithZero.{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))))) p)
 Case conversion may be inaccurate. Consider using '#align polynomial.monic.irreducible_of_degree_eq_one Polynomial.Monic.irreducible_of_degree_eq_oneₓ'. -/
 theorem Monic.irreducible_of_degree_eq_one (hp1 : degree p = 1) (hm : Monic p) : Irreducible p :=
   (hm.prime_of_degree_eq_one hp1).Irreducible
@@ -634,7 +634,7 @@ theorem Monic.irreducible_of_degree_eq_one (hp1 : degree p = 1) (hm : Monic p) :
 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {q : 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) -> (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) q) -> (Associated.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p q) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p q)
 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {q : 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) -> (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) q) -> (Associated.{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))) (Semiring.toMonoidWithZero.{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))))) p q) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p q)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {q : 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) -> (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) q) -> (Associated.{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))) (Semiring.toMonoidWithZero.{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))))) p q) -> (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p q)
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_of_monic_of_associated Polynomial.eq_of_monic_of_associatedₓ'. -/
 theorem eq_of_monic_of_associated (hp : p.Monic) (hq : q.Monic) (hpq : Associated p q) : p = q :=
   by
@@ -662,7 +662,7 @@ theorem rootMultiplicity_mul {p q : R[X]} {x : R} (hpq : p * q ≠ 0) :
 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))] {x : R}, Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 x (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) x))) (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))] {x : R}, Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 x (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) x) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) x))) (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))] {x : R}, Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 x (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) x) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) x))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))
 Case conversion may be inaccurate. Consider using '#align polynomial.root_multiplicity_X_sub_C_self Polynomial.rootMultiplicity_X_sub_C_selfₓ'. -/
 theorem rootMultiplicity_X_sub_C_self {x : R} : rootMultiplicity x (X - C x) = 1 := by
   rw [root_multiplicity_eq_multiplicity, dif_neg (X_sub_C_ne_zero x),
@@ -673,7 +673,7 @@ theorem rootMultiplicity_X_sub_C_self {x : R} : rootMultiplicity x (X - C x) = 1
 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))] {x : R} {y : R}, Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 x (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) y))) (ite.{1} Nat (Eq.{succ u1} R x y) (Classical.propDecidable (Eq.{succ u1} R x y)) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {x : R} {y : R}, Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 x (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) y) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) y))) (ite.{1} Nat (Eq.{succ u1} R x y) (Classical.propDecidable (Eq.{succ u1} R x y)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {x : R} {y : R}, Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 x (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) y) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) y))) (ite.{1} Nat (Eq.{succ u1} R x y) (Classical.propDecidable (Eq.{succ u1} R x y)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))
 Case conversion may be inaccurate. Consider using '#align polynomial.root_multiplicity_X_sub_C Polynomial.rootMultiplicity_X_sub_Cₓ'. -/
 theorem rootMultiplicity_X_sub_C {x y : R} :
     rootMultiplicity x (X - C y) = if x = y then 1 else 0 :=
@@ -688,7 +688,7 @@ theorem rootMultiplicity_X_sub_C {x y : 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))] (a : R) (n : Nat), Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 a (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) n)) n
 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))] (a : R) (n : Nat), Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 a (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) n)) n
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (a : R) (n : Nat), Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 a (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) n)) n
 Case conversion may be inaccurate. Consider using '#align polynomial.root_multiplicity_X_sub_C_pow Polynomial.rootMultiplicity_X_sub_C_powₓ'. -/
 /-- The multiplicity of `a` as root of `(X - a) ^ n` is `n`. -/
 theorem rootMultiplicity_X_sub_C_pow (a : R) (n : ℕ) : rootMultiplicity a ((X - C a) ^ n) = n :=
@@ -705,7 +705,7 @@ theorem rootMultiplicity_X_sub_C_pow (a : R) (n : ℕ) : rootMultiplicity a ((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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (Exists.{succ u1} (Multiset.{u1} R) (fun (s : Multiset.{u1} R) => And (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s)) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) (forall (a : R), Eq.{1} Nat (Multiset.count.{u1} R (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)) a s) (Polynomial.rootMultiplicity.{u1} R _inst_1 a 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) -> (Exists.{succ u1} (Multiset.{u1} R) (fun (s : Multiset.{u1} R) => And (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s)) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) (forall (a : R), Eq.{1} Nat (Multiset.count.{u1} R (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)) a s) (Polynomial.rootMultiplicity.{u1} R _inst_1 a 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))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) -> (Exists.{succ u1} (Multiset.{u1} R) (fun (s : Multiset.{u1} R) => And (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s)) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) (forall (a : R), Eq.{1} Nat (Multiset.count.{u1} R (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)) a s) (Polynomial.rootMultiplicity.{u1} R _inst_1 a p))))
 Case conversion may be inaccurate. Consider using '#align polynomial.exists_multiset_roots Polynomial.exists_multiset_rootsₓ'. -/
 theorem exists_multiset_roots :
     ∀ {p : R[X]} (hp : p ≠ 0),
@@ -768,7 +768,7 @@ theorem roots_zero : (0 : R[X]).roots = 0 :=
 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))) (Polynomial.degree.{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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))) (Polynomial.degree.{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))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.card_roots Polynomial.card_rootsₓ'. -/
 theorem card_roots (hp0 : p ≠ 0) : ((roots p).card : WithBot ℕ) ≤ degree p :=
   by
@@ -781,7 +781,7 @@ theorem card_roots (hp0 : p ≠ 0) : ((roots p).card : WithBot ℕ) ≤ degree p
 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))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), LE.le.{0} Nat Nat.hasLe (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{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))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) instLENat (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{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))] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) instLENat (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)
 Case conversion may be inaccurate. Consider using '#align polynomial.card_roots' Polynomial.card_roots'ₓ'. -/
 theorem card_roots' (p : R[X]) : p.roots.card ≤ natDegree p :=
   by
@@ -794,7 +794,7 @@ theorem card_roots' (p : R[X]) : p.roots.card ≤ natDegree p :=
 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {a : R}, (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 (CommRing.toRing.{u1} R _inst_1)) p)) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a))))) (Polynomial.degree.{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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {a : R}, (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 (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a))))) (Polynomial.degree.{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))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {a : R}, (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 (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a))))) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.card_roots_sub_C Polynomial.card_roots_sub_Cₓ'. -/
 theorem card_roots_sub_C {p : R[X]} {a : R} (hp0 : 0 < degree p) :
     ((p - C a).roots.card : WithBot ℕ) ≤ degree p :=
@@ -809,7 +809,7 @@ theorem card_roots_sub_C {p : R[X]} {a : R} (hp0 : 0 < degree p) :
 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {a : R}, (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 (CommRing.toRing.{u1} R _inst_1)) p)) -> (LE.le.{0} Nat Nat.hasLe (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a)))) (Polynomial.natDegree.{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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {a : R}, (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 (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) -> (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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 (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (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))) a)))) instLENat (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a)))) (Polynomial.natDegree.{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))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {a : R}, (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 (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) -> (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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 (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (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))) a)))) instLENat (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a)))) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.card_roots_sub_C' Polynomial.card_roots_sub_C'ₓ'. -/
 theorem card_roots_sub_C' {p : R[X]} {a : R} (hp0 : 0 < degree p) :
     (p - C a).roots.card ≤ natDegree p :=
@@ -905,7 +905,7 @@ theorem roots_mul {p q : R[X]} (hpq : p * q ≠ 0) : (p * q).roots = p.roots + q
 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) q (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) p q) -> (LE.le.{u1} (Multiset.{u1} R) (Preorder.toLE.{u1} (Multiset.{u1} R) (PartialOrder.toPreorder.{u1} (Multiset.{u1} R) (Multiset.partialOrder.{u1} R))) (Polynomial.roots.{u1} R _inst_1 _inst_2 p) (Polynomial.roots.{u1} R _inst_1 _inst_2 q))
 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) q (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) -> (Dvd.dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) p q) -> (LE.le.{u1} (Multiset.{u1} R) (Preorder.toLE.{u1} (Multiset.{u1} R) (PartialOrder.toPreorder.{u1} (Multiset.{u1} R) (Multiset.instPartialOrderMultiset.{u1} R))) (Polynomial.roots.{u1} R _inst_1 _inst_2 p) (Polynomial.roots.{u1} R _inst_1 _inst_2 q))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) q (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) -> (Dvd.dvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) p q) -> (LE.le.{u1} (Multiset.{u1} R) (Preorder.toLE.{u1} (Multiset.{u1} R) (PartialOrder.toPreorder.{u1} (Multiset.{u1} R) (Multiset.instPartialOrderMultiset.{u1} R))) (Polynomial.roots.{u1} R _inst_1 _inst_2 p) (Polynomial.roots.{u1} R _inst_1 _inst_2 q))
 Case conversion may be inaccurate. Consider using '#align polynomial.roots.le_of_dvd Polynomial.roots.le_of_dvdₓ'. -/
 theorem roots.le_of_dvd (h : q ≠ 0) : p ∣ q → roots p ≤ roots q :=
   by
@@ -917,7 +917,7 @@ theorem roots.le_of_dvd (h : q ≠ 0) : p ∣ q → roots p ≤ roots q :=
 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {a : R} {x : R}, Iff (Membership.Mem.{u1, u1} R (Multiset.{u1} R) (Multiset.hasMem.{u1} R) x (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a)))) (And (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a)) (Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x p) a))
 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {a : R} {x : R}, Iff (Membership.mem.{u1, u1} R (Multiset.{u1} R) (Multiset.instMembershipMultiset.{u1} R) x (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a)))) (And (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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 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(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))) a)) (Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x p) a))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {a : R} {x : R}, Iff (Membership.mem.{u1, u1} R (Multiset.{u1} R) (Multiset.instMembershipMultiset.{u1} R) x (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a)))) (And (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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))) a)) (Eq.{succ u1} R (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) x p) a))
 Case conversion may be inaccurate. Consider using '#align polynomial.mem_roots_sub_C' Polynomial.mem_roots_sub_C'ₓ'. -/
 theorem mem_roots_sub_C' {p : R[X]} {a x : R} : x ∈ (p - C a).roots ↔ p ≠ C a ∧ p.eval x = a := by
   rw [mem_roots', is_root.def, sub_ne_zero, eval_sub, sub_eq_zero, eval_C]
@@ -927,7 +927,7 @@ theorem mem_roots_sub_C' {p : R[X]} {a x : R} : x ∈ (p - C a).roots ↔ p ≠
 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {a : R} {x : R}, (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 (CommRing.toRing.{u1} R _inst_1)) p)) -> (Iff (Membership.Mem.{u1, u1} R (Multiset.{u1} R) (Multiset.hasMem.{u1} R) x (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a)))) (Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x p) a))
 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {a : R} {x : R}, (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 (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) -> (Iff (Membership.mem.{u1, u1} R (Multiset.{u1} R) (Multiset.instMembershipMultiset.{u1} R) x (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a)))) (Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x p) a))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {a : R} {x : R}, (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 (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) -> (Iff (Membership.mem.{u1, u1} R (Multiset.{u1} R) (Multiset.instMembershipMultiset.{u1} R) x (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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))) a)))) (Eq.{succ u1} R (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) x p) a))
 Case conversion may be inaccurate. Consider using '#align polynomial.mem_roots_sub_C Polynomial.mem_roots_sub_Cₓ'. -/
 theorem mem_roots_sub_C {p : R[X]} {a x : R} (hp0 : 0 < degree p) :
     x ∈ (p - C a).roots ↔ p.eval x = a :=
@@ -938,7 +938,7 @@ theorem mem_roots_sub_C {p : R[X]} {a x : R} (hp0 : 0 < degree p) :
 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))] (r : R), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) r))) (Singleton.singleton.{u1, u1} R (Multiset.{u1} R) (Multiset.hasSingleton.{u1} R) r)
 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))] (r : R), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{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))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) r))) (Singleton.singleton.{u1, u1} R (Multiset.{u1} R) (Multiset.instSingletonMultiset.{u1} R) r)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (r : R), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{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))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) r))) (Singleton.singleton.{u1, u1} R (Multiset.{u1} R) (Multiset.instSingletonMultiset.{u1} R) r)
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_X_sub_C Polynomial.roots_X_sub_Cₓ'. -/
 @[simp]
 theorem roots_X_sub_C (r : R) : roots (X - C r) = {r} :=
@@ -951,7 +951,7 @@ theorem roots_X_sub_C (r : R) : roots (X - C r) = {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))], Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Singleton.singleton.{u1, u1} R (Multiset.{u1} R) (Multiset.hasSingleton.{u1} R) (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 (CommRing.toRing.{u1} R _inst_1))))))))))
 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))], Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Singleton.singleton.{u1, u1} R (Multiset.{u1} R) (Multiset.instSingletonMultiset.{u1} R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{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 (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Singleton.singleton.{u1, u1} R (Multiset.{u1} R) (Multiset.instSingletonMultiset.{u1} R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_X Polynomial.roots_Xₓ'. -/
 @[simp]
 theorem roots_X : roots (X : R[X]) = {0} := by rw [← roots_X_sub_C, C_0, sub_zero]
@@ -961,7 +961,7 @@ theorem roots_X : roots (X : R[X]) = {0} := by rw [← roots_X_sub_C, C_0, sub_z
 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))] (x : R), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (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))) x)) (OfNat.ofNat.{u1} (Multiset.{u1} R) 0 (OfNat.mk.{u1} (Multiset.{u1} R) 0 (Zero.zero.{u1} (Multiset.{u1} R) (Multiset.hasZero.{u1} R))))
 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))] (x : R), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (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))) x)) (OfNat.ofNat.{u1} (Multiset.{u1} R) 0 (Zero.toOfNat0.{u1} (Multiset.{u1} R) (Multiset.instZeroMultiset.{u1} R)))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (x : R), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (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))) x)) (OfNat.ofNat.{u1} (Multiset.{u1} R) 0 (Zero.toOfNat0.{u1} (Multiset.{u1} R) (Multiset.instZeroMultiset.{u1} R)))
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_C Polynomial.roots_Cₓ'. -/
 @[simp]
 theorem roots_C (x : R) : (C x).roots = 0 :=
@@ -982,7 +982,7 @@ theorem roots_one : (1 : R[X]).roots = ∅ :=
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{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 (CommRing.toRing.{u1} R _inst_1)))))))))) -> (Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HMul.hMul.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (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))) a) p)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))) -> (Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (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))) a) p)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))) -> (Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (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))) a) p)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_C_mul Polynomial.roots_C_mulₓ'. -/
 @[simp]
 theorem roots_C_mul (p : R[X]) (ha : a ≠ 0) : (C a * p).roots = p.roots := by
@@ -995,7 +995,7 @@ theorem roots_C_mul (p : R[X]) (ha : a ≠ 0) : (C a * p).roots = p.roots := by
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{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 (CommRing.toRing.{u1} R _inst_1)))))))))) -> (Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (SMul.smul.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SMulZeroClass.toHasSmul.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.smulZeroClass.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (SMulWithZero.toSmulZeroClass.{u1, u1} R R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) a p)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))) -> (Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSMul.hSMul.{u1, u1, u1} 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))) (instHSMul.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Algebra.toSMul.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) a p)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))) -> (Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSMul.hSMul.{u1, u1, u1} 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))) (instHSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) a p)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_smul_nonzero Polynomial.roots_smul_nonzeroₓ'. -/
 @[simp]
 theorem roots_smul_nonzero (p : R[X]) (ha : a ≠ 0) : (a • p).roots = p.roots := by
@@ -1025,7 +1025,7 @@ theorem roots_multiset_prod (m : Multiset R[X]) : (0 : R[X]) ∉ m → m.Prod.ro
 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))] {ι : Type.{u2}} (f : ι -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (s : Finset.{u2} ι), (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Finset.prod.{u1, u2} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) s f) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{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 (Finset.prod.{u1, u2} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) s f)) (Multiset.bind.{u2, u1} ι R (Finset.val.{u2} ι s) (fun (i : ι) => Polynomial.roots.{u1} R _inst_1 _inst_2 (f i))))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] [_inst_2 : IsDomain.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))] {ι : Type.{u1}} (f : ι -> (Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) (s : Finset.{u1} ι), (Ne.{succ u2} (Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Finset.prod.{u2, u1} (Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Polynomial.commRing.{u2} R _inst_1)) s f) (OfNat.ofNat.{u2} (Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Polynomial.zero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) -> (Eq.{succ u2} (Multiset.{u2} R) (Polynomial.roots.{u2} R _inst_1 _inst_2 (Finset.prod.{u2, u1} (Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Polynomial.commRing.{u2} R _inst_1)) s f)) (Multiset.bind.{u1, u2} ι R (Finset.val.{u1} ι s) (fun (i : ι) => Polynomial.roots.{u2} R _inst_1 _inst_2 (f i))))
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] [_inst_2 : IsDomain.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))] {ι : Type.{u1}} (f : ι -> (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (s : Finset.{u1} ι), (Ne.{succ u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Finset.prod.{u2, u1} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.commRing.{u2} R _inst_1)) s f) (OfNat.ofNat.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.zero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) -> (Eq.{succ u2} (Multiset.{u2} R) (Polynomial.roots.{u2} R _inst_1 _inst_2 (Finset.prod.{u2, u1} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.commRing.{u2} R _inst_1)) s f)) (Multiset.bind.{u1, u2} ι R (Finset.val.{u1} ι s) (fun (i : ι) => Polynomial.roots.{u2} R _inst_1 _inst_2 (f i))))
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_prod Polynomial.roots_prodₓ'. -/
 theorem roots_prod {ι : Type _} (f : ι → R[X]) (s : Finset ι) :
     s.Prod f ≠ 0 → (s.Prod f).roots = s.val.bind fun i => roots (f i) :=
@@ -1038,7 +1038,7 @@ theorem roots_prod {ι : Type _} (f : ι → R[X]) (s : Finset ι) :
 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))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (n : Nat), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) p n)) (SMul.smul.{0, u1} Nat (Multiset.{u1} R) (AddMonoid.SMul.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) n (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))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (n : Nat), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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))))))) p n)) (HSMul.hSMul.{0, u1, u1} Nat (Multiset.{u1} R) (Multiset.{u1} R) (instHSMul.{0, u1} Nat (Multiset.{u1} R) (AddMonoid.SMul.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) n (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))] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (n : Nat), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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))))))) p n)) (HSMul.hSMul.{0, u1, u1} Nat (Multiset.{u1} R) (Multiset.{u1} R) (instHSMul.{0, u1} Nat (Multiset.{u1} R) (AddMonoid.SMul.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) n (Polynomial.roots.{u1} R _inst_1 _inst_2 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_pow Polynomial.roots_powₓ'. -/
 @[simp]
 theorem roots_pow (p : R[X]) (n : ℕ) : (p ^ n).roots = n • p.roots :=
@@ -1056,7 +1056,7 @@ theorem roots_pow (p : R[X]) (n : ℕ) : (p ^ n).roots = n • p.roots :=
 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))] (n : Nat), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) n)) (SMul.smul.{0, u1} Nat (Multiset.{u1} R) (AddMonoid.SMul.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) n (Singleton.singleton.{u1, u1} R (Multiset.{u1} R) (Multiset.hasSingleton.{u1} R) (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 (CommRing.toRing.{u1} R _inst_1)))))))))))
 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))] (n : Nat), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) n)) (HSMul.hSMul.{0, u1, u1} Nat (Multiset.{u1} R) (Multiset.{u1} R) (instHSMul.{0, u1} Nat (Multiset.{u1} R) (AddMonoid.SMul.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) n (Singleton.singleton.{u1, u1} R (Multiset.{u1} R) (Multiset.instSingletonMultiset.{u1} R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (n : Nat), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n)) (HSMul.hSMul.{0, u1, u1} Nat (Multiset.{u1} R) (Multiset.{u1} R) (instHSMul.{0, u1} Nat (Multiset.{u1} R) (AddMonoid.SMul.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) n (Singleton.singleton.{u1, u1} R (Multiset.{u1} R) (Multiset.instSingletonMultiset.{u1} R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_X_pow Polynomial.roots_X_powₓ'. -/
 theorem roots_X_pow (n : ℕ) : (X ^ n : R[X]).roots = n • {0} := by rw [roots_pow, roots_X]
 #align polynomial.roots_X_pow Polynomial.roots_X_pow
@@ -1065,7 +1065,7 @@ theorem roots_X_pow (n : ℕ) : (X ^ n : R[X]).roots = n • {0} := by rw [roots
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{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 (CommRing.toRing.{u1} R _inst_1)))))))))) -> (forall (n : Nat), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HMul.hMul.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (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))) a) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) n))) (SMul.smul.{0, u1} Nat (Multiset.{u1} R) (AddMonoid.SMul.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) n (Singleton.singleton.{u1, u1} R (Multiset.{u1} R) (Multiset.hasSingleton.{u1} R) (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 (CommRing.toRing.{u1} R _inst_1))))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))) -> (forall (n : Nat), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (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))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (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))) a) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) n))) (HSMul.hSMul.{0, u1, u1} Nat (Multiset.{u1} R) (Multiset.{u1} R) (instHSMul.{0, u1} Nat (Multiset.{u1} R) (AddMonoid.SMul.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) n (Singleton.singleton.{u1, u1} R (Multiset.{u1} R) (Multiset.instSingletonMultiset.{u1} R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))))))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))], (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))) -> (forall (n : Nat), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (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))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (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))) a) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n))) (HSMul.hSMul.{0, u1, u1} Nat (Multiset.{u1} R) (Multiset.{u1} R) (instHSMul.{0, u1} Nat (Multiset.{u1} R) (AddMonoid.SMul.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) n (Singleton.singleton.{u1, u1} R (Multiset.{u1} R) (Multiset.instSingletonMultiset.{u1} R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_C_mul_X_pow Polynomial.roots_C_mul_X_powₓ'. -/
 theorem roots_C_mul_X_pow (ha : a ≠ 0) (n : ℕ) : (C a * X ^ n).roots = n • {0} := by
   rw [roots_C_mul _ ha, roots_X_pow]
@@ -1075,7 +1075,7 @@ theorem roots_C_mul_X_pow (ha : a ≠ 0) (n : ℕ) : (C a * X ^ n).roots = n •
 lean 3 declaration is
   forall {R : Type.{u1}} {a : R} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{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 (CommRing.toRing.{u1} R _inst_1)))))))))) -> (forall (n : Nat), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (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)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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)))))) (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)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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)))))) (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))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (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} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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)))))) (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.monomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) n) a)) (SMul.smul.{0, u1} Nat (Multiset.{u1} R) (AddMonoid.SMul.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) n (Singleton.singleton.{u1, u1} R (Multiset.{u1} R) (Multiset.hasSingleton.{u1} R) (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 (CommRing.toRing.{u1} R _inst_1))))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {a : R} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))) -> (forall (n : Nat), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (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)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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)))))) (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))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (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} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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)))))) (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.monomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) n) a)) (HSMul.hSMul.{0, u1, u1} Nat (Multiset.{u1} R) (Multiset.{u1} R) (instHSMul.{0, u1} Nat (Multiset.{u1} R) (AddMonoid.SMul.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) n (Singleton.singleton.{u1, u1} R (Multiset.{u1} R) (Multiset.instSingletonMultiset.{u1} R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))))))
+  forall {R : Type.{u1}} {a : R} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))], (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))) -> (forall (n : Nat), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (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)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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)))))) (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))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (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} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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)))))) (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.monomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) n) a)) (HSMul.hSMul.{0, u1, u1} Nat (Multiset.{u1} R) (Multiset.{u1} R) (instHSMul.{0, u1} Nat (Multiset.{u1} R) (AddMonoid.SMul.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) n (Singleton.singleton.{u1, u1} R (Multiset.{u1} R) (Multiset.instSingletonMultiset.{u1} R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_monomial Polynomial.roots_monomialₓ'. -/
 @[simp]
 theorem roots_monomial (ha : a ≠ 0) (n : ℕ) : (monomial n a).roots = n • {0} := by
@@ -1086,7 +1086,7 @@ theorem roots_monomial (ha : a ≠ 0) (n : ℕ) : (monomial n a).roots = n • {
 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))] (s : Finset.{u1} R), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (Finset.prod.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) s (fun (a : R) => HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)))) (Finset.val.{u1} R s)
 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))] (s : Finset.{u1} R), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (Finset.prod.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) s (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)))) (Finset.val.{u1} R s)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (s : Finset.{u1} R), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (Finset.prod.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) s (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)))) (Finset.val.{u1} R s)
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_prod_X_sub_C Polynomial.roots_prod_X_sub_Cₓ'. -/
 theorem roots_prod_X_sub_C (s : Finset R) : (s.Prod fun a => X - C a).roots = s.val :=
   (roots_prod (fun a => X - C a) s (prod_ne_zero_iff.mpr fun a _ => X_sub_C_ne_zero a)).trans
@@ -1097,7 +1097,7 @@ theorem roots_prod_X_sub_C (s : Finset R) : (s.Prod fun a => X - C a).roots = s.
 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))] (s : Multiset.{u1} R), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) s))) s
 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))] (s : Multiset.{u1} R), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) s))) s
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (s : Multiset.{u1} R), Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) s))) s
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_multiset_prod_X_sub_C Polynomial.roots_multiset_prod_X_sub_Cₓ'. -/
 @[simp]
 theorem roots_multiset_prod_X_sub_C (s : Multiset R) : (s.map fun a => X - C a).Prod.roots = s :=
@@ -1113,7 +1113,7 @@ theorem roots_multiset_prod_X_sub_C (s : Multiset R) : (s.map fun a => X - C a).
 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))] (s : Multiset.{u1} R), Eq.{1} Nat (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) s))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s)
 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))] (s : Multiset.{u1} R), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) s))) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (s : Multiset.{u1} R), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) s) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) s))) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s)
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_multiset_prod_X_sub_C_eq_card Polynomial.natDegree_multiset_prod_X_sub_C_eq_cardₓ'. -/
 @[simp]
 theorem natDegree_multiset_prod_X_sub_C_eq_card (s : Multiset R) :
@@ -1130,7 +1130,7 @@ theorem natDegree_multiset_prod_X_sub_C_eq_card (s : Multiset 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))] {n : Nat}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n) -> (forall (a : R), LE.le.{0} Nat Nat.hasLe (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) n) (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))) a)))) n)
 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))] {n : Nat}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) -> (forall (a : R), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) n) (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 (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (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))) a)))) instLENat (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) n) (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))) a)))) n)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {n : Nat}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) -> (forall (a : R), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n) (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 (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (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))) a)))) instLENat (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n) (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))) a)))) n)
 Case conversion may be inaccurate. Consider using '#align polynomial.card_roots_X_pow_sub_C Polynomial.card_roots_X_pow_sub_Cₓ'. -/
 theorem card_roots_X_pow_sub_C {n : ℕ} (hn : 0 < n) (a : R) :
     (roots ((X : R[X]) ^ n - C a)).card ≤ n :=
@@ -1155,7 +1155,7 @@ def nthRoots (n : ℕ) (a : R) : Multiset 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))] {n : Nat}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n) -> (forall {a : R} {x : R}, Iff (Membership.Mem.{u1, u1} R (Multiset.{u1} R) (Multiset.hasMem.{u1} R) x (Polynomial.nthRoots.{u1} R _inst_1 _inst_2 n a)) (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) x n) a))
 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))] {n : Nat}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) -> (forall {a : R} {x : R}, Iff (Membership.mem.{u1, u1} R (Multiset.{u1} R) (Multiset.instMembershipMultiset.{u1} R) x (Polynomial.nthRoots.{u1} R _inst_1 _inst_2 n a)) (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) x n) a))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {n : Nat}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) -> (forall {a : R} {x : R}, Iff (Membership.mem.{u1, u1} R (Multiset.{u1} R) (Multiset.instMembershipMultiset.{u1} R) x (Polynomial.nthRoots.{u1} R _inst_1 _inst_2 n a)) (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) x n) a))
 Case conversion may be inaccurate. Consider using '#align polynomial.mem_nth_roots Polynomial.mem_nthRootsₓ'. -/
 @[simp]
 theorem mem_nthRoots {n : ℕ} (hn : 0 < n) {a x : R} : x ∈ nthRoots n a ↔ x ^ n = a := by
@@ -1174,7 +1174,7 @@ theorem nthRoots_zero (r : R) : nthRoots 0 r = 0 := by
 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))] (n : Nat) (a : R), LE.le.{0} Nat Nat.hasLe (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) (Polynomial.nthRoots.{u1} R _inst_1 _inst_2 n a)) n
 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))] (n : Nat) (a : R), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.nthRoots.{u1} R _inst_1 _inst_2 n a)) instLENat (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.nthRoots.{u1} R _inst_1 _inst_2 n a)) n
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (n : Nat) (a : R), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.nthRoots.{u1} R _inst_1 _inst_2 n a)) instLENat (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.nthRoots.{u1} R _inst_1 _inst_2 n a)) n
 Case conversion may be inaccurate. Consider using '#align polynomial.card_nth_roots Polynomial.card_nthRootsₓ'. -/
 theorem card_nthRoots (n : ℕ) (a : R) : (nthRoots n a).card ≤ n :=
   if hn : n = 0 then
@@ -1195,7 +1195,7 @@ theorem card_nthRoots (n : ℕ) (a : R) : (nthRoots n a).card ≤ n :=
 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))] {r : R}, Iff (Eq.{succ u1} (Multiset.{u1} R) (Polynomial.nthRoots.{u1} R _inst_1 _inst_2 (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) r) (OfNat.ofNat.{u1} (Multiset.{u1} R) 0 (OfNat.mk.{u1} (Multiset.{u1} R) 0 (Zero.zero.{u1} (Multiset.{u1} R) (Multiset.hasZero.{u1} R))))) (Not (IsSquare.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) r))
 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))] {r : R}, Iff (Eq.{succ u1} (Multiset.{u1} R) (Polynomial.nthRoots.{u1} R _inst_1 _inst_2 (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) r) (OfNat.ofNat.{u1} (Multiset.{u1} R) 0 (Zero.toOfNat0.{u1} (Multiset.{u1} R) (Multiset.instZeroMultiset.{u1} R)))) (Not (IsSquare.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) r))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {r : R}, Iff (Eq.{succ u1} (Multiset.{u1} R) (Polynomial.nthRoots.{u1} R _inst_1 _inst_2 (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) r) (OfNat.ofNat.{u1} (Multiset.{u1} R) 0 (Zero.toOfNat0.{u1} (Multiset.{u1} R) (Multiset.instZeroMultiset.{u1} R)))) (Not (IsSquare.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) r))
 Case conversion may be inaccurate. Consider using '#align polynomial.nth_roots_two_eq_zero_iff Polynomial.nthRoots_two_eq_zero_iffₓ'. -/
 @[simp]
 theorem nthRoots_two_eq_zero_iff {r : R} : nthRoots 2 r = 0 ↔ ¬IsSquare r := by
@@ -1214,7 +1214,7 @@ def nthRootsFinset (n : ℕ) (R : Type _) [CommRing R] [IsDomain R] : Finset 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))] {n : Nat}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n) -> (forall {x : R}, Iff (Membership.Mem.{u1, u1} R (Finset.{u1} R) (Finset.hasMem.{u1} R) x (Polynomial.nthRootsFinset.{u1} n R _inst_1 _inst_2)) (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) x n) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))
 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))] {n : Nat}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) -> (forall {x : R}, Iff (Membership.mem.{u1, u1} R (Finset.{u1} R) (Finset.instMembershipFinset.{u1} R) x (Polynomial.nthRootsFinset.{u1} n R _inst_1 _inst_2)) (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) x n) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_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))] {n : Nat}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) -> (forall {x : R}, Iff (Membership.mem.{u1, u1} R (Finset.{u1} R) (Finset.instMembershipFinset.{u1} R) x (Polynomial.nthRootsFinset.{u1} n R _inst_1 _inst_2)) (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) x n) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.mem_nth_roots_finset Polynomial.mem_nthRootsFinsetₓ'. -/
 @[simp]
 theorem mem_nthRootsFinset {n : ℕ} (h : 0 < n) {x : R} : x ∈ nthRootsFinset n R ↔ x ^ (n : ℕ) = 1 :=
@@ -1239,7 +1239,7 @@ theorem Monic.comp (hp : p.Monic) (hq : q.Monic) (h : q.natDegree ≠ 0) : (p.co
 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))] {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) -> (forall (r : R), Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.comp.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p (HAdd.hAdd.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHAdd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) r))))
 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))] {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) -> (forall (r : R), Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.comp.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{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))) (instHAdd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.add'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) r))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {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) -> (forall (r : R), Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{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))) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) r))))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic.comp_X_add_C Polynomial.Monic.comp_X_add_Cₓ'. -/
 theorem Monic.comp_X_add_C (hp : p.Monic) (r : R) : (p.comp (X + C r)).Monic :=
   by
@@ -1252,7 +1252,7 @@ theorem Monic.comp_X_add_C (hp : p.Monic) (r : R) : (p.comp (X + C r)).Monic :=
 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))] {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) -> (forall (r : R), Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.comp.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) r))))
 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))] {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) -> (forall (r : R), Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.comp.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{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))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) r))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {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) -> (forall (r : R), Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{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))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) r))))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic.comp_X_sub_C Polynomial.Monic.comp_X_sub_Cₓ'. -/
 theorem Monic.comp_X_sub_C (hp : p.Monic) (r : R) : (p.comp (X - C r)).Monic := by
   simpa using hp.comp_X_add_C (-r)
@@ -1262,7 +1262,7 @@ theorem Monic.comp_X_sub_C (hp : p.Monic) (r : R) : (p.comp (X - C r)).Monic :=
 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))] (c : Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (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))) (SMul.smul.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SMulZeroClass.toHasSmul.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.smulZeroClass.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (SMulWithZero.toSmulZeroClass.{u1, u1} R R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Polynomial.coeff.{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))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (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))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (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))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (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))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (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))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) c) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) p) (HMul.hMul.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{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))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (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))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (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))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (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))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (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))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) c) 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))] (c : 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))) (Semiring.toMonoidWithZero.{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)))))) (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))) (HSMul.hSMul.{u1, u1, u1} 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))) (instHSMul.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Algebra.toSMul.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.coeff.{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))) (Semiring.toMonoidWithZero.{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))))) c) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) p) (HMul.hMul.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{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))) (Semiring.toMonoidWithZero.{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))))) c) 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))] (c : Units.{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))) (Semiring.toMonoidWithZero.{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)))))) (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))) (HSMul.hSMul.{u1, u1, u1} 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))) (instHSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.coeff.{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))) (Semiring.toMonoidWithZero.{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))))) c) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) p) (HMul.hMul.{u1, 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))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{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))) (Semiring.toMonoidWithZero.{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))))) c) p)
 Case conversion may be inaccurate. Consider using '#align polynomial.units_coeff_zero_smul Polynomial.units_coeff_zero_smulₓ'. -/
 theorem units_coeff_zero_smul (c : R[X]ˣ) (p : R[X]) : (c : R[X]).coeff 0 • p = c * p := by
   rw [← Polynomial.C_mul', ← Polynomial.eq_C_of_degree_eq_zero (degree_coe_units c)]
@@ -1272,7 +1272,7 @@ theorem units_coeff_zero_smul (c : R[X]ˣ) (p : R[X]) : (c : R[X]).coeff 0 • p
 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))] (u : Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{1} Nat (Polynomial.natDegree.{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))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (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))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (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))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (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))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (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))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) u)) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] (u : 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))) (Semiring.toMonoidWithZero.{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)))))), Eq.{1} Nat (Polynomial.natDegree.{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))) (Semiring.toMonoidWithZero.{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))))) u)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (u : Units.{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))) (Semiring.toMonoidWithZero.{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)))))), Eq.{1} Nat (Polynomial.natDegree.{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))) (Semiring.toMonoidWithZero.{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))))) u)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_coe_units Polynomial.natDegree_coe_unitsₓ'. -/
 @[simp]
 theorem natDegree_coe_units (u : R[X]ˣ) : natDegree (u : R[X]) = 0 :=
@@ -1283,7 +1283,7 @@ theorem natDegree_coe_units (u : R[X]ˣ) : natDegree (u : R[X]) = 0 :=
 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Iff (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.comp.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p q) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Or (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (And (Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) q (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) p) (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 (CommRing.toRing.{u1} R _inst_1)))))))))) (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) q (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))) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) q (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Iff (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.comp.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p q) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Or (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (And (Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) q (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) p) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))) (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) q (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))) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) q (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, Iff (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.comp.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p q) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Or (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (And (Eq.{succ u1} R (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) q (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) p) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))) (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) q (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))) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) q (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.comp_eq_zero_iff Polynomial.comp_eq_zero_iffₓ'. -/
 theorem comp_eq_zero_iff : p.comp q = 0 ↔ p = 0 ∨ p.eval (q.coeff 0) = 0 ∧ q = C (q.coeff 0) :=
   by
@@ -1306,7 +1306,7 @@ theorem comp_eq_zero_iff : p.comp q = 0 ↔ p = 0 ∨ p.eval (q.coeff 0) = 0 ∧
 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 : Infinite.{succ u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (forall (x : R), Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x p) (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 (CommRing.toRing.{u1} R _inst_1)))))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))
 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 : Infinite.{succ u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (forall (x : R), Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x p) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_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 : Infinite.{succ u1} R] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), (forall (x : R), Eq.{succ u1} R (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) x p) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))) -> (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.zero_of_eval_zero Polynomial.zero_of_eval_zeroₓ'. -/
 theorem zero_of_eval_zero [Infinite R] (p : R[X]) (h : ∀ x, p.eval x = 0) : p = 0 := by
   classical by_contra hp <;>
@@ -1341,7 +1341,7 @@ def rootSet (p : T[X]) (S) [CommRing S] [IsDomain S] [Algebra T S] : Set S :=
 lean 3 declaration is
   forall {T : Type.{u1}} [_inst_3 : CommRing.{u1} T] (p : Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) (S : Type.{u2}) [_inst_4 : CommRing.{u2} S] [_inst_5 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_6 : Algebra.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))], Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} T _inst_3 p S _inst_4 _inst_5 _inst_6) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} S) (Set.{u2} S) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} S) (Set.{u2} S) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} S) (Set.{u2} S) (Finset.Set.hasCoeT.{u2} S))) (Multiset.toFinset.{u2} S (fun (a : S) (b : S) => Classical.propDecidable (Eq.{succ u2} S a b)) (Polynomial.roots.{u2} S _inst_4 _inst_5 (Polynomial.map.{u1, u2} T S (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (algebraMap.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6) p))))
 but is expected to have type
-  forall {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] (p : Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (S : Type.{u1}) [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))], Eq.{succ u1} (Set.{u1} S) (Polynomial.rootSet.{u2, u1} T _inst_3 p S _inst_4 _inst_5 _inst_6) (Finset.toSet.{u1} S (Multiset.toFinset.{u1} S (fun (a : S) (b : S) => Classical.propDecidable (Eq.{succ u1} S a b)) (Polynomial.roots.{u1} S _inst_4 _inst_5 (Polynomial.map.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (algebraMap.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) _inst_6) p))))
+  forall {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] (p : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (S : Type.{u1}) [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))], Eq.{succ u1} (Set.{u1} S) (Polynomial.rootSet.{u2, u1} T _inst_3 p S _inst_4 _inst_5 _inst_6) (Finset.toSet.{u1} S (Multiset.toFinset.{u1} S (fun (a : S) (b : S) => Classical.propDecidable (Eq.{succ u1} S a b)) (Polynomial.roots.{u1} S _inst_4 _inst_5 (Polynomial.map.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (algebraMap.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6) p))))
 Case conversion may be inaccurate. Consider using '#align polynomial.root_set_def Polynomial.rootSet_defₓ'. -/
 theorem rootSet_def (p : T[X]) (S) [CommRing S] [IsDomain S] [Algebra T S] :
     p.rootSet S = (p.map (algebraMap T S)).roots.toFinset :=
@@ -1352,7 +1352,7 @@ theorem rootSet_def (p : T[X]) (S) [CommRing S] [IsDomain S] [Algebra T S] :
 lean 3 declaration is
   forall {S : Type.{u1}} {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))] (a : T), Eq.{succ u1} (Set.{u1} S) (Polynomial.rootSet.{u2, u1} T _inst_3 (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} T (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))))) (fun (_x : RingHom.{u2, u2} T (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))))) => T -> (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3)))) (RingHom.hasCoeToFun.{u2, u2} T (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))))) (Polynomial.C.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) a) S _inst_4 _inst_5 _inst_6) (EmptyCollection.emptyCollection.{u1} (Set.{u1} S) (Set.hasEmptyc.{u1} S))
 but is expected to have type
-  forall {S : Type.{u1}} {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))] (a : T), Eq.{succ u1} (Set.{u1} S) (Polynomial.rootSet.{u2, u1} T _inst_3 (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} T (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))))) T (fun (_x : T) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : T) => Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} T (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))))) T (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} T (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))))) T (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} T (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))))) T (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u2} T (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3)))))))) (Polynomial.C.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) a) S _inst_4 _inst_5 _inst_6) (EmptyCollection.emptyCollection.{u1} (Set.{u1} S) (Set.instEmptyCollectionSet.{u1} S))
+  forall {S : Type.{u1}} {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))] (a : T), Eq.{succ u1} (Set.{u1} S) (Polynomial.rootSet.{u2, u1} T _inst_3 (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) T (fun (_x : T) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : T) => Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (Polynomial.C.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) a) S _inst_4 _inst_5 _inst_6) (EmptyCollection.emptyCollection.{u1} (Set.{u1} S) (Set.instEmptyCollectionSet.{u1} S))
 Case conversion may be inaccurate. Consider using '#align polynomial.root_set_C Polynomial.rootSet_Cₓ'. -/
 @[simp]
 theorem rootSet_C [CommRing S] [IsDomain S] [Algebra T S] (a : T) : (C a).rootSet S = ∅ := by
@@ -1363,7 +1363,7 @@ theorem rootSet_C [CommRing S] [IsDomain S] [Algebra T S] (a : T) : (C a).rootSe
 lean 3 declaration is
   forall {T : Type.{u1}} [_inst_3 : CommRing.{u1} T] (S : Type.{u2}) [_inst_4 : CommRing.{u2} S] [_inst_5 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_6 : Algebra.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))], Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} T _inst_3 (OfNat.ofNat.{u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) 0 (OfNat.mk.{u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) 0 (Zero.zero.{u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) (Polynomial.zero.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3)))))) S _inst_4 _inst_5 _inst_6) (EmptyCollection.emptyCollection.{u2} (Set.{u2} S) (Set.hasEmptyc.{u2} S))
 but is expected to have type
-  forall {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] (S : Type.{u1}) [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))], Eq.{succ u1} (Set.{u1} S) (Polynomial.rootSet.{u2, u1} T _inst_3 (OfNat.ofNat.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Polynomial.zero.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))))) S _inst_4 _inst_5 _inst_6) (EmptyCollection.emptyCollection.{u1} (Set.{u1} S) (Set.instEmptyCollectionSet.{u1} S))
+  forall {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] (S : Type.{u1}) [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))], Eq.{succ u1} (Set.{u1} S) (Polynomial.rootSet.{u2, u1} T _inst_3 (OfNat.ofNat.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.zero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) S _inst_4 _inst_5 _inst_6) (EmptyCollection.emptyCollection.{u1} (Set.{u1} S) (Set.instEmptyCollectionSet.{u1} S))
 Case conversion may be inaccurate. Consider using '#align polynomial.root_set_zero Polynomial.rootSet_zeroₓ'. -/
 @[simp]
 theorem rootSet_zero (S) [CommRing S] [IsDomain S] [Algebra T S] : (0 : T[X]).rootSet S = ∅ := by
@@ -1381,7 +1381,7 @@ instance rootSetFintype (p : T[X]) (S : Type _) [CommRing S] [IsDomain S] [Algeb
 lean 3 declaration is
   forall {T : Type.{u1}} [_inst_3 : CommRing.{u1} T] (p : Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) (S : Type.{u2}) [_inst_4 : CommRing.{u2} S] [_inst_5 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_6 : Algebra.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))], Set.Finite.{u2} S (Polynomial.rootSet.{u1, u2} T _inst_3 p S _inst_4 _inst_5 _inst_6)
 but is expected to have type
-  forall {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] (p : Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (S : Type.{u1}) [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))], Set.Finite.{u1} S (Polynomial.rootSet.{u2, u1} T _inst_3 p S _inst_4 _inst_5 _inst_6)
+  forall {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] (p : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (S : Type.{u1}) [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))], Set.Finite.{u1} S (Polynomial.rootSet.{u2, u1} T _inst_3 p S _inst_4 _inst_5 _inst_6)
 Case conversion may be inaccurate. Consider using '#align polynomial.root_set_finite Polynomial.rootSet_finiteₓ'. -/
 theorem rootSet_finite (p : T[X]) (S : Type _) [CommRing S] [IsDomain S] [Algebra T S] :
     (p.rootSet S).Finite :=
@@ -1392,7 +1392,7 @@ theorem rootSet_finite (p : T[X]) (S : Type _) [CommRing S] [IsDomain S] [Algebr
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_4 : Semiring.{u1} R] [_inst_5 : CommRing.{u2} S] [_inst_6 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5))] (m : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_4) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))) (d : Nat) {U : Set.{u1} R}, (Set.Finite.{u1} R U) -> (Set.Finite.{u2} S (Set.unionᵢ.{u2, succ u1} S (Polynomial.{u1} R _inst_4) (fun (f : Polynomial.{u1} R _inst_4) => Set.unionᵢ.{u2, 0} S (And (LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R _inst_4 f) d) (forall (i : Nat), Membership.Mem.{u1, u1} R (Set.{u1} R) (Set.hasMem.{u1} R) (Polynomial.coeff.{u1} R _inst_4 f i) U)) (fun (hf : And (LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R _inst_4 f) d) (forall (i : Nat), Membership.Mem.{u1, u1} R (Set.{u1} R) (Set.hasMem.{u1} R) (Polynomial.coeff.{u1} R _inst_4 f i) U)) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} S) (Set.{u2} S) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} S) (Set.{u2} S) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} S) (Set.{u2} S) (Finset.Set.hasCoeT.{u2} S))) (Multiset.toFinset.{u2} S (fun (a : S) (b : S) => Classical.propDecidable (Eq.{succ u2} S a b)) (Polynomial.roots.{u2} S _inst_5 _inst_6 (Polynomial.map.{u1, u2} R S _inst_4 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5)) m f)))))))
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_4 : Semiring.{u2} R] [_inst_5 : CommRing.{u1} S] [_inst_6 : IsDomain.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_5))] (m : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_4) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))) (d : Nat) {U : Set.{u2} R}, (Set.Finite.{u2} R U) -> (Set.Finite.{u1} S (Set.unionᵢ.{u1, succ u2} S (Polynomial.{u2} R _inst_4) (fun (f : Polynomial.{u2} R _inst_4) => Set.unionᵢ.{u1, 0} S (And (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u2} R _inst_4 f) d) (forall (i : Nat), Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) (Polynomial.coeff.{u2} R _inst_4 f i) U)) (fun (hf : And (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u2} R _inst_4 f) d) (forall (i : Nat), Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) (Polynomial.coeff.{u2} R _inst_4 f i) U)) => Finset.toSet.{u1} S (Multiset.toFinset.{u1} S (fun (a : S) (b : S) => Classical.propDecidable (Eq.{succ u1} S a b)) (Polynomial.roots.{u1} S _inst_5 _inst_6 (Polynomial.map.{u2, u1} R S _inst_4 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_5)) m f)))))))
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_4 : Semiring.{u2} R] [_inst_5 : CommRing.{u1} S] [_inst_6 : IsDomain.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))] (m : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_4) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (d : Nat) {U : Set.{u2} R}, (Set.Finite.{u2} R U) -> (Set.Finite.{u1} S (Set.unionᵢ.{u1, succ u2} S (Polynomial.{u2} R _inst_4) (fun (f : Polynomial.{u2} R _inst_4) => Set.unionᵢ.{u1, 0} S (And (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u2} R _inst_4 f) d) (forall (i : Nat), Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) (Polynomial.coeff.{u2} R _inst_4 f i) U)) (fun (hf : And (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u2} R _inst_4 f) d) (forall (i : Nat), Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) (Polynomial.coeff.{u2} R _inst_4 f i) U)) => Finset.toSet.{u1} S (Multiset.toFinset.{u1} S (fun (a : S) (b : S) => Classical.propDecidable (Eq.{succ u1} S a b)) (Polynomial.roots.{u1} S _inst_5 _inst_6 (Polynomial.map.{u2, u1} R S _inst_4 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)) m f)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.bUnion_roots_finite Polynomial.bUnion_roots_finiteₓ'. -/
 /-- The set of roots of all polynomials of bounded degree and having coefficients in a finite set
 is finite. -/
@@ -1416,7 +1416,7 @@ theorem bUnion_roots_finite {R S : Type _} [Semiring R] [CommRing S] [IsDomain S
 lean 3 declaration is
   forall {T : Type.{u1}} [_inst_3 : CommRing.{u1} T] {p : Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))} {S : Type.{u2}} [_inst_4 : CommRing.{u2} S] [_inst_5 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_6 : Algebra.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] {a : S}, Iff (Membership.Mem.{u2, u2} S (Set.{u2} S) (Set.hasMem.{u2} S) a (Polynomial.rootSet.{u1, u2} T _inst_3 p S _inst_4 _inst_5 _inst_6)) (And (Ne.{succ u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))) (Polynomial.map.{u1, u2} T S (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (algebraMap.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6) p) (OfNat.ofNat.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))) 0 (OfNat.mk.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))) 0 (Zero.zero.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))) (Polynomial.zero.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))))) (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} T (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) S (CommRing.toCommSemiring.{u1} T _inst_3) (Polynomial.semiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} T T (CommRing.toCommSemiring.{u1} T _inst_3) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Algebra.id.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) (fun (_x : AlgHom.{u1, u1, u2} T (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) S (CommRing.toCommSemiring.{u1} T _inst_3) (Polynomial.semiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} T T (CommRing.toCommSemiring.{u1} T _inst_3) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Algebra.id.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) => (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) -> S) ([anonymous].{u1, u1, u2} T (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) S (CommRing.toCommSemiring.{u1} T _inst_3) (Polynomial.semiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} T T (CommRing.toCommSemiring.{u1} T _inst_3) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Algebra.id.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) (Polynomial.aeval.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6 a) p) (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_4)))))))))))
 but is expected to have type
-  forall {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] {p : Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))} {S : Type.{u1}} [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))] {a : S}, Iff (Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) a (Polynomial.rootSet.{u2, u1} T _inst_3 p S _inst_4 _inst_5 _inst_6)) (And (Ne.{succ u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))) (Polynomial.map.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (algebraMap.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) _inst_6) p) (OfNat.ofNat.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))) (Polynomial.zero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)))))) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (fun (_x : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (SMulZeroClass.toSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toZero.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (SMulZeroClass.toSMul.{u2, u1} T S (AddMonoid.toZero.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))))))) (DistribSMul.toSMulZeroClass.{u2, u1} T S (AddMonoid.toAddZeroClass.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))))))) (DistribMulAction.toDistribSMul.{u2, u1} T S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)))))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6 (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6))))) (Polynomial.aeval.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) _inst_6 a) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (IsDomain.toCancelCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) _inst_4) _inst_5)))))))
+  forall {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] {p : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))} {S : Type.{u1}} [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))] {a : S}, Iff (Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) a (Polynomial.rootSet.{u2, u1} T _inst_3 p S _inst_4 _inst_5 _inst_6)) (And (Ne.{succ u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))) (Polynomial.map.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (algebraMap.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6) p) (OfNat.ofNat.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))) (Polynomial.zero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))))) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (fun (_x : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (SMulZeroClass.toSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toZero.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (SMulZeroClass.toSMul.{u2, u1} T S (AddMonoid.toZero.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))))) (DistribSMul.toSMulZeroClass.{u2, u1} T S (AddMonoid.toAddZeroClass.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))))) (DistribMulAction.toDistribSMul.{u2, u1} T S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6 (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6))))) (Polynomial.aeval.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6 a) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (IsDomain.toCancelCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) _inst_4) _inst_5)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.mem_root_set' Polynomial.mem_rootSet'ₓ'. -/
 theorem mem_rootSet' {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Algebra T S] {a : S} :
     a ∈ p.rootSet S ↔ p.map (algebraMap T S) ≠ 0 ∧ aeval a p = 0 := by
@@ -1428,7 +1428,7 @@ theorem mem_rootSet' {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Algebra
 lean 3 declaration is
   forall {T : Type.{u1}} [_inst_3 : CommRing.{u1} T] {p : Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))} {S : Type.{u2}} [_inst_4 : CommRing.{u2} S] [_inst_5 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_6 : Algebra.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_7 : NoZeroSMulDivisors.{u1, u2} T S (MulZeroClass.toHasZero.{u1} T (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} T (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} T (NonAssocRing.toNonUnitalNonAssocRing.{u1} T (Ring.toNonAssocRing.{u1} T (CommRing.toRing.{u1} T _inst_3)))))) (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_4)))))) (SMulZeroClass.toHasSmul.{u1, u2} T S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} T S (MulZeroClass.toHasZero.{u1} T (MulZeroOneClass.toMulZeroClass.{u1} T (MonoidWithZero.toMulZeroOneClass.{u1} T (Semiring.toMonoidWithZero.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} T S (Semiring.toMonoidWithZero.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) (Module.toMulActionWithZero.{u1, u2} T S (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))) (Algebra.toModule.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6)))))] {a : S}, Iff (Membership.Mem.{u2, u2} S (Set.{u2} S) (Set.hasMem.{u2} S) a (Polynomial.rootSet.{u1, u2} T _inst_3 p S _inst_4 _inst_5 _inst_6)) (And (Ne.{succ u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) p (OfNat.ofNat.{u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) 0 (OfNat.mk.{u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) 0 (Zero.zero.{u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) (Polynomial.zero.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))))))) (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} T (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) S (CommRing.toCommSemiring.{u1} T _inst_3) (Polynomial.semiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} T T (CommRing.toCommSemiring.{u1} T _inst_3) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Algebra.id.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) (fun (_x : AlgHom.{u1, u1, u2} T (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) S (CommRing.toCommSemiring.{u1} T _inst_3) (Polynomial.semiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} T T (CommRing.toCommSemiring.{u1} T _inst_3) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Algebra.id.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) => (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) -> S) ([anonymous].{u1, u1, u2} T (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) S (CommRing.toCommSemiring.{u1} T _inst_3) (Polynomial.semiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} T T (CommRing.toCommSemiring.{u1} T _inst_3) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Algebra.id.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) (Polynomial.aeval.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6 a) p) (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_4)))))))))))
 but is expected to have type
-  forall {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] {p : Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))} {S : Type.{u1}} [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))] [_inst_7 : NoZeroSMulDivisors.{u2, u1} T S (CommMonoidWithZero.toZero.{u2} T (CommSemiring.toCommMonoidWithZero.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommMonoidWithZero.toZero.{u1} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} S (IsDomain.toCancelCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4) _inst_5))) (Algebra.toSMul.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) _inst_6)] {a : S}, Iff (Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) a (Polynomial.rootSet.{u2, u1} T _inst_3 p S _inst_4 _inst_5 _inst_6)) (And (Ne.{succ u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) p (OfNat.ofNat.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Polynomial.zero.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3)))))) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (fun (_x : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (SMulZeroClass.toSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toZero.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (SMulZeroClass.toSMul.{u2, u1} T S (AddMonoid.toZero.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))))))) (DistribSMul.toSMulZeroClass.{u2, u1} T S (AddMonoid.toAddZeroClass.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))))))) (DistribMulAction.toDistribSMul.{u2, u1} T S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)))))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6 (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6))))) (Polynomial.aeval.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) _inst_6 a) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (IsDomain.toCancelCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) _inst_4) _inst_5)))))))
+  forall {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] {p : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))} {S : Type.{u1}} [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))] [_inst_7 : NoZeroSMulDivisors.{u2, u1} T S (CommMonoidWithZero.toZero.{u2} T (CommSemiring.toCommMonoidWithZero.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommMonoidWithZero.toZero.{u1} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} S (IsDomain.toCancelCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4) _inst_5))) (Algebra.toSMul.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6)] {a : S}, Iff (Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) a (Polynomial.rootSet.{u2, u1} T _inst_3 p S _inst_4 _inst_5 _inst_6)) (And (Ne.{succ u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) p (OfNat.ofNat.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.zero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (fun (_x : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (SMulZeroClass.toSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toZero.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (SMulZeroClass.toSMul.{u2, u1} T S (AddMonoid.toZero.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))))) (DistribSMul.toSMulZeroClass.{u2, u1} T S (AddMonoid.toAddZeroClass.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))))) (DistribMulAction.toDistribSMul.{u2, u1} T S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6 (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6))))) (Polynomial.aeval.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6 a) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (IsDomain.toCancelCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) _inst_4) _inst_5)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.mem_root_set Polynomial.mem_rootSetₓ'. -/
 theorem mem_rootSet {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Algebra T S]
     [NoZeroSMulDivisors T S] {a : S} : a ∈ p.rootSet S ↔ p ≠ 0 ∧ aeval a p = 0 := by
@@ -1440,7 +1440,7 @@ theorem mem_rootSet {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Algebra T
 lean 3 declaration is
   forall {T : Type.{u1}} [_inst_3 : CommRing.{u1} T] {p : Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))} {S : Type.{u2}} [_inst_4 : CommRing.{u2} S] [_inst_5 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_6 : Algebra.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_7 : NoZeroSMulDivisors.{u1, u2} T S (MulZeroClass.toHasZero.{u1} T (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} T (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} T (NonAssocRing.toNonUnitalNonAssocRing.{u1} T (Ring.toNonAssocRing.{u1} T (CommRing.toRing.{u1} T _inst_3)))))) (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_4)))))) (SMulZeroClass.toHasSmul.{u1, u2} T S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} T S (MulZeroClass.toHasZero.{u1} T (MulZeroOneClass.toMulZeroClass.{u1} T (MonoidWithZero.toMulZeroOneClass.{u1} T (Semiring.toMonoidWithZero.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} T S (Semiring.toMonoidWithZero.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) (Module.toMulActionWithZero.{u1, u2} T S (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))) (Algebra.toModule.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6)))))], (Ne.{succ u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) p (OfNat.ofNat.{u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) 0 (OfNat.mk.{u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) 0 (Zero.zero.{u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) (Polynomial.zero.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))))))) -> (forall {a : S}, Iff (Membership.Mem.{u2, u2} S (Set.{u2} S) (Set.hasMem.{u2} S) a (Polynomial.rootSet.{u1, u2} T _inst_3 p S _inst_4 _inst_5 _inst_6)) (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} T (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) S (CommRing.toCommSemiring.{u1} T _inst_3) (Polynomial.semiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} T T (CommRing.toCommSemiring.{u1} T _inst_3) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Algebra.id.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) (fun (_x : AlgHom.{u1, u1, u2} T (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) S (CommRing.toCommSemiring.{u1} T _inst_3) (Polynomial.semiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} T T (CommRing.toCommSemiring.{u1} T _inst_3) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Algebra.id.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) => (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) -> S) ([anonymous].{u1, u1, u2} T (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) S (CommRing.toCommSemiring.{u1} T _inst_3) (Polynomial.semiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} T T (CommRing.toCommSemiring.{u1} T _inst_3) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Algebra.id.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) (Polynomial.aeval.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6 a) p) (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_4)))))))))))
 but is expected to have type
-  forall {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] {p : Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))} {S : Type.{u1}} [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))] [_inst_7 : NoZeroSMulDivisors.{u2, u1} T S (CommMonoidWithZero.toZero.{u2} T (CommSemiring.toCommMonoidWithZero.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommMonoidWithZero.toZero.{u1} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} S (IsDomain.toCancelCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4) _inst_5))) (Algebra.toSMul.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) _inst_6)], (Ne.{succ u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) p (OfNat.ofNat.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Polynomial.zero.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3)))))) -> (forall {a : S}, Iff (Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) a (Polynomial.rootSet.{u2, u1} T _inst_3 p S _inst_4 _inst_5 _inst_6)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (fun (_x : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (SMulZeroClass.toSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toZero.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (SMulZeroClass.toSMul.{u2, u1} T S (AddMonoid.toZero.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))))))) (DistribSMul.toSMulZeroClass.{u2, u1} T S (AddMonoid.toAddZeroClass.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))))))) (DistribMulAction.toDistribSMul.{u2, u1} T S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)))))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6 (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6))))) (Polynomial.aeval.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) _inst_6 a) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (IsDomain.toCancelCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) _inst_4) _inst_5)))))))
+  forall {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] {p : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))} {S : Type.{u1}} [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))] [_inst_7 : NoZeroSMulDivisors.{u2, u1} T S (CommMonoidWithZero.toZero.{u2} T (CommSemiring.toCommMonoidWithZero.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommMonoidWithZero.toZero.{u1} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} S (IsDomain.toCancelCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4) _inst_5))) (Algebra.toSMul.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6)], (Ne.{succ u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) p (OfNat.ofNat.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.zero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) -> (forall {a : S}, Iff (Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) a (Polynomial.rootSet.{u2, u1} T _inst_3 p S _inst_4 _inst_5 _inst_6)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (fun (_x : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (SMulZeroClass.toSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toZero.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (SMulZeroClass.toSMul.{u2, u1} T S (AddMonoid.toZero.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))))) (DistribSMul.toSMulZeroClass.{u2, u1} T S (AddMonoid.toAddZeroClass.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))))) (DistribMulAction.toDistribSMul.{u2, u1} T S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6 (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6))))) (Polynomial.aeval.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4)) _inst_6 a) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (IsDomain.toCancelCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) _inst_4) _inst_5)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.mem_root_set_of_ne Polynomial.mem_rootSet_of_neₓ'. -/
 theorem mem_rootSet_of_ne {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Algebra T S]
     [NoZeroSMulDivisors T S] (hp : p ≠ 0) {a : S} : a ∈ p.rootSet S ↔ aeval a p = 0 :=
@@ -1451,7 +1451,7 @@ theorem mem_rootSet_of_ne {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Alg
 lean 3 declaration is
   forall {T : Type.{u1}} [_inst_3 : CommRing.{u1} T] {p : Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))} {S : Type.{u2}} {S' : Type.{u3}} [_inst_4 : CommRing.{u2} S] [_inst_5 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_6 : Algebra.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_7 : CommRing.{u3} S'] [_inst_8 : IsDomain.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7))] [_inst_9 : Algebra.{u1, u3} T S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7))], ((Eq.{succ u3} (Polynomial.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7))) (Polynomial.map.{u1, u3} T S' (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)) (algebraMap.{u1, u3} T S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)) _inst_9) p) (OfNat.ofNat.{u3} (Polynomial.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7))) 0 (OfNat.mk.{u3} (Polynomial.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7))) 0 (Zero.zero.{u3} (Polynomial.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7))) (Polynomial.zero.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7))))))) -> (Eq.{succ u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))) (Polynomial.map.{u1, u2} T S (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (algebraMap.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6) p) (OfNat.ofNat.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))) 0 (OfNat.mk.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))) 0 (Zero.zero.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))) (Polynomial.zero.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) -> (forall (f : AlgHom.{u1, u2, u3} T S S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)) _inst_6 _inst_9), Set.MapsTo.{u2, u3} S S' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} T S S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)) _inst_6 _inst_9) (fun (_x : AlgHom.{u1, u2, u3} T S S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)) _inst_6 _inst_9) => S -> S') ([anonymous].{u1, u2, u3} T S S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)) _inst_6 _inst_9) f) (Polynomial.rootSet.{u1, u2} T _inst_3 p S _inst_4 _inst_5 _inst_6) (Polynomial.rootSet.{u1, u3} T _inst_3 p S' _inst_7 _inst_8 _inst_9))
 but is expected to have type
-  forall {T : Type.{u3}} [_inst_3 : CommRing.{u3} T] {p : Polynomial.{u3} T (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_3))} {S : Type.{u2}} {S' : Type.{u1}} [_inst_4 : CommRing.{u2} S] [_inst_5 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_6 : Algebra.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_7 : CommRing.{u1} S'] [_inst_8 : IsDomain.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7))] [_inst_9 : Algebra.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7))], ((Eq.{succ u1} (Polynomial.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7))) (Polynomial.map.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) (algebraMap.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_9) p) (OfNat.ofNat.{u1} (Polynomial.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7))) (Polynomial.zero.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)))))) -> (Eq.{succ u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))) (Polynomial.map.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (algebraMap.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6) p) (OfNat.ofNat.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))) (Polynomial.zero.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))))) -> (forall (f : AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_6 _inst_9), Set.MapsTo.{u2, u1} S S' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_6 _inst_9) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_6 _inst_9) T S S' (SMulZeroClass.toSMul.{u3, u2} T S (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))))) (DistribSMul.toSMulZeroClass.{u3, u2} T S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))))) (DistribMulAction.toDistribSMul.{u3, u2} T S (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))) (Module.toDistribMulAction.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))) (Algebra.toModule.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6))))) (SMulZeroClass.toSMul.{u3, u1} T S' (AddMonoid.toZero.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7))))))) (DistribSMul.toSMulZeroClass.{u3, u1} T S' (AddMonoid.toAddZeroClass.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7))))))) (DistribMulAction.toDistribSMul.{u3, u1} T S' (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)))))) (Module.toDistribMulAction.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7))))) (Algebra.toModule.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_6 _inst_9) T S S' (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)))))) (Module.toDistribMulAction.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))) (Algebra.toModule.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6)) (Module.toDistribMulAction.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7))))) (Algebra.toModule.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_9)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_6 _inst_9) T S S' (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)))) (Module.toDistribMulAction.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))) (Algebra.toModule.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6)) (Module.toDistribMulAction.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7))))) (Algebra.toModule.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_9)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_6 _inst_9 (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_6 _inst_9) (AlgHom.algHomClass.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_6 _inst_9))))) f) (Polynomial.rootSet.{u3, u2} T _inst_3 p S _inst_4 _inst_5 _inst_6) (Polynomial.rootSet.{u3, u1} T _inst_3 p S' _inst_7 _inst_8 _inst_9))
+  forall {T : Type.{u3}} [_inst_3 : CommRing.{u3} T] {p : Polynomial.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3))} {S : Type.{u2}} {S' : Type.{u1}} [_inst_4 : CommRing.{u2} S] [_inst_5 : IsDomain.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))] [_inst_6 : Algebra.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))] [_inst_7 : CommRing.{u1} S'] [_inst_8 : IsDomain.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))] [_inst_9 : Algebra.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))], ((Eq.{succ u1} (Polynomial.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))) (Polynomial.map.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) (algebraMap.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_9) p) (OfNat.ofNat.{u1} (Polynomial.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))) (Polynomial.zero.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)))))) -> (Eq.{succ u2} (Polynomial.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))) (Polynomial.map.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (algebraMap.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) _inst_6) p) (OfNat.ofNat.{u2} (Polynomial.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))) (Polynomial.zero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))))) -> (forall (f : AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9), Set.MapsTo.{u2, u1} S S' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) T S S' (SMulZeroClass.toSMul.{u3, u2} T S (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))))) (DistribSMul.toSMulZeroClass.{u3, u2} T S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))))) (DistribMulAction.toDistribSMul.{u3, u2} T S (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))))) (Module.toDistribMulAction.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))) (Algebra.toModule.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) _inst_6))))) (SMulZeroClass.toSMul.{u3, u1} T S' (AddMonoid.toZero.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))))) (DistribSMul.toSMulZeroClass.{u3, u1} T S' (AddMonoid.toAddZeroClass.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))))) (DistribMulAction.toDistribSMul.{u3, u1} T S' (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)))))) (Module.toDistribMulAction.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))) (Algebra.toModule.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) T S S' (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)))))) (Module.toDistribMulAction.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))) (Algebra.toModule.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) _inst_6)) (Module.toDistribMulAction.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))) (Algebra.toModule.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_9)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) T S S' (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)))) (Module.toDistribMulAction.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))) (Algebra.toModule.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) _inst_6)) (Module.toDistribMulAction.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))) (Algebra.toModule.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_9)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9 (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) (AlgHom.algHomClass.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9))))) f) (Polynomial.rootSet.{u3, u2} T _inst_3 p S _inst_4 _inst_5 _inst_6) (Polynomial.rootSet.{u3, u1} T _inst_3 p S' _inst_7 _inst_8 _inst_9))
 Case conversion may be inaccurate. Consider using '#align polynomial.root_set_maps_to' Polynomial.rootSet_maps_to'ₓ'. -/
 theorem rootSet_maps_to' {p : T[X]} {S S'} [CommRing S] [IsDomain S] [Algebra T S] [CommRing S']
     [IsDomain S'] [Algebra T S'] (hp : p.map (algebraMap T S') = 0 → p.map (algebraMap T S) = 0)
@@ -1479,7 +1479,7 @@ theorem aeval_eq_zero_of_mem_rootSet {p : T[X]} [CommRing S] [IsDomain S] [Algeb
 lean 3 declaration is
   forall {T : Type.{u1}} [_inst_3 : CommRing.{u1} T] {p : Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))} {S : Type.{u2}} {S' : Type.{u3}} [_inst_4 : CommRing.{u2} S] [_inst_5 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_6 : Algebra.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_7 : CommRing.{u3} S'] [_inst_8 : IsDomain.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7))] [_inst_9 : Algebra.{u1, u3} T S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7))] [_inst_10 : NoZeroSMulDivisors.{u1, u3} T S' (MulZeroClass.toHasZero.{u1} T (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} T (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} T (NonAssocRing.toNonUnitalNonAssocRing.{u1} T (Ring.toNonAssocRing.{u1} T (CommRing.toRing.{u1} T _inst_3)))))) (MulZeroClass.toHasZero.{u3} S' (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} S' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} S' (NonAssocRing.toNonUnitalNonAssocRing.{u3} S' (Ring.toNonAssocRing.{u3} S' (CommRing.toRing.{u3} S' _inst_7)))))) (SMulZeroClass.toHasSmul.{u1, u3} T S' (AddZeroClass.toHasZero.{u3} S' (AddMonoid.toAddZeroClass.{u3} S' (AddCommMonoid.toAddMonoid.{u3} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S' (Semiring.toNonAssocSemiring.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} T S' (MulZeroClass.toHasZero.{u1} T (MulZeroOneClass.toMulZeroClass.{u1} T (MonoidWithZero.toMulZeroOneClass.{u1} T (Semiring.toMonoidWithZero.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)))))) (AddZeroClass.toHasZero.{u3} S' (AddMonoid.toAddZeroClass.{u3} S' (AddCommMonoid.toAddMonoid.{u3} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S' (Semiring.toNonAssocSemiring.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} T S' (Semiring.toMonoidWithZero.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (AddZeroClass.toHasZero.{u3} S' (AddMonoid.toAddZeroClass.{u3} S' (AddCommMonoid.toAddMonoid.{u3} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S' (Semiring.toNonAssocSemiring.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)))))))) (Module.toMulActionWithZero.{u1, u3} T S' (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S' (Semiring.toNonAssocSemiring.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7))))) (Algebra.toModule.{u1, u3} T S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)) _inst_9)))))] (f : AlgHom.{u1, u2, u3} T S S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)) _inst_6 _inst_9), Set.MapsTo.{u2, u3} S S' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} T S S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)) _inst_6 _inst_9) (fun (_x : AlgHom.{u1, u2, u3} T S S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)) _inst_6 _inst_9) => S -> S') ([anonymous].{u1, u2, u3} T S S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)) _inst_6 _inst_9) f) (Polynomial.rootSet.{u1, u2} T _inst_3 p S _inst_4 _inst_5 _inst_6) (Polynomial.rootSet.{u1, u3} T _inst_3 p S' _inst_7 _inst_8 _inst_9)
 but is expected to have type
-  forall {T : Type.{u3}} [_inst_3 : CommRing.{u3} T] {p : Polynomial.{u3} T (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_3))} {S : Type.{u2}} {S' : Type.{u1}} [_inst_4 : CommRing.{u2} S] [_inst_5 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_6 : Algebra.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_7 : CommRing.{u1} S'] [_inst_8 : IsDomain.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7))] [_inst_9 : Algebra.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7))] [_inst_10 : NoZeroSMulDivisors.{u3, u1} T S' (CommMonoidWithZero.toZero.{u3} T (CommSemiring.toCommMonoidWithZero.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3))) (CommMonoidWithZero.toZero.{u1} S' (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} S' (IsDomain.toCancelCommMonoidWithZero.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_9)] (f : AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_6 _inst_9), Set.MapsTo.{u2, u1} S S' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_6 _inst_9) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_6 _inst_9) T S S' (SMulZeroClass.toSMul.{u3, u2} T S (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))))) (DistribSMul.toSMulZeroClass.{u3, u2} T S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))))) (DistribMulAction.toDistribSMul.{u3, u2} T S (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))) (Module.toDistribMulAction.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))) (Algebra.toModule.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6))))) (SMulZeroClass.toSMul.{u3, u1} T S' (AddMonoid.toZero.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7))))))) (DistribSMul.toSMulZeroClass.{u3, u1} T S' (AddMonoid.toAddZeroClass.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7))))))) (DistribMulAction.toDistribSMul.{u3, u1} T S' (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)))))) (Module.toDistribMulAction.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7))))) (Algebra.toModule.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_6 _inst_9) T S S' (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)))))) (Module.toDistribMulAction.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))) (Algebra.toModule.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6)) (Module.toDistribMulAction.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7))))) (Algebra.toModule.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_9)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_6 _inst_9) T S S' (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)))) (Module.toDistribMulAction.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))) (Algebra.toModule.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6)) (Module.toDistribMulAction.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7))))) (Algebra.toModule.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_9)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_6 _inst_9 (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_6 _inst_9) (AlgHom.algHomClass.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_6 _inst_9))))) f) (Polynomial.rootSet.{u3, u2} T _inst_3 p S _inst_4 _inst_5 _inst_6) (Polynomial.rootSet.{u3, u1} T _inst_3 p S' _inst_7 _inst_8 _inst_9)
+  forall {T : Type.{u3}} [_inst_3 : CommRing.{u3} T] {p : Polynomial.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3))} {S : Type.{u2}} {S' : Type.{u1}} [_inst_4 : CommRing.{u2} S] [_inst_5 : IsDomain.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))] [_inst_6 : Algebra.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))] [_inst_7 : CommRing.{u1} S'] [_inst_8 : IsDomain.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))] [_inst_9 : Algebra.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))] [_inst_10 : NoZeroSMulDivisors.{u3, u1} T S' (CommMonoidWithZero.toZero.{u3} T (CommSemiring.toCommMonoidWithZero.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3))) (CommMonoidWithZero.toZero.{u1} S' (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} S' (IsDomain.toCancelCommMonoidWithZero.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_9)] (f : AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9), Set.MapsTo.{u2, u1} S S' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) T S S' (SMulZeroClass.toSMul.{u3, u2} T S (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))))) (DistribSMul.toSMulZeroClass.{u3, u2} T S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))))) (DistribMulAction.toDistribSMul.{u3, u2} T S (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))))) (Module.toDistribMulAction.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))) (Algebra.toModule.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) _inst_6))))) (SMulZeroClass.toSMul.{u3, u1} T S' (AddMonoid.toZero.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))))) (DistribSMul.toSMulZeroClass.{u3, u1} T S' (AddMonoid.toAddZeroClass.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))))) (DistribMulAction.toDistribSMul.{u3, u1} T S' (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)))))) (Module.toDistribMulAction.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))) (Algebra.toModule.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) T S S' (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)))))) (Module.toDistribMulAction.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))) (Algebra.toModule.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) _inst_6)) (Module.toDistribMulAction.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))) (Algebra.toModule.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_9)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) T S S' (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)))) (Module.toDistribMulAction.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))) (Algebra.toModule.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) _inst_6)) (Module.toDistribMulAction.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7))))) (Algebra.toModule.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_9)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9 (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9) (AlgHom.algHomClass.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (CommSemiring.toSemiring.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7)) _inst_6 _inst_9))))) f) (Polynomial.rootSet.{u3, u2} T _inst_3 p S _inst_4 _inst_5 _inst_6) (Polynomial.rootSet.{u3, u1} T _inst_3 p S' _inst_7 _inst_8 _inst_9)
 Case conversion may be inaccurate. Consider using '#align polynomial.root_set_maps_to Polynomial.rootSet_mapsToₓ'. -/
 theorem rootSet_mapsTo {p : T[X]} {S S'} [CommRing S] [IsDomain S] [Algebra T S] [CommRing S']
     [IsDomain S'] [Algebra T S'] [NoZeroSMulDivisors T S'] (f : S →ₐ[T] S') :
@@ -1497,7 +1497,7 @@ end Roots
 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))] (u : Units.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Ne.{succ u1} R (Polynomial.coeff.{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))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (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))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (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))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (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))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (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))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) u) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (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 (CommRing.toRing.{u1} R _inst_1)))))))))
 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))] (u : 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))) (Semiring.toMonoidWithZero.{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)))))), Ne.{succ u1} R (Polynomial.coeff.{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))) (Semiring.toMonoidWithZero.{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))))) u) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (u : Units.{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))) (Semiring.toMonoidWithZero.{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)))))), Ne.{succ u1} R (Polynomial.coeff.{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))) (Semiring.toMonoidWithZero.{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))))) u) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.coeff_coe_units_zero_ne_zero Polynomial.coeff_coe_units_zero_ne_zeroₓ'. -/
 theorem coeff_coe_units_zero_ne_zero (u : R[X]ˣ) : coeff (u : R[X]) 0 ≠ 0 :=
   by
@@ -1510,7 +1510,7 @@ theorem coeff_coe_units_zero_ne_zero (u : R[X]ˣ) : coeff (u : R[X]) 0 ≠ 0 :=
 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Associated.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p q) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) q))
 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Associated.{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))) (Semiring.toMonoidWithZero.{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))))) p q) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) q))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Associated.{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))) (Semiring.toMonoidWithZero.{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))))) p q) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) q))
 Case conversion may be inaccurate. Consider using '#align polynomial.degree_eq_degree_of_associated Polynomial.degree_eq_degree_of_associatedₓ'. -/
 theorem degree_eq_degree_of_associated (h : Associated p q) : degree p = degree q :=
   by
@@ -1522,7 +1522,7 @@ theorem degree_eq_degree_of_associated (h : Associated p q) : degree p = degree
 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p) -> (forall {x : R}, (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p x) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{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))))))
 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Irreducible.{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))) (Semiring.toMonoidWithZero.{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))))) p) -> (forall {x : R}, (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p x) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) (OfNat.ofNat.{0} (WithBot.{0} Nat) 1 (One.toOfNat1.{0} (WithBot.{0} Nat) (WithBot.one.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Irreducible.{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))) (Semiring.toMonoidWithZero.{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))))) p) -> (forall {x : R}, (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p x) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p) (OfNat.ofNat.{0} (WithBot.{0} Nat) 1 (One.toOfNat1.{0} (WithBot.{0} Nat) (WithBot.one.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.degree_eq_one_of_irreducible_of_root Polynomial.degree_eq_one_of_irreducible_of_rootₓ'. -/
 theorem degree_eq_one_of_irreducible_of_root (hi : Irreducible p) {x : R} (hx : IsRoot p x) :
     degree p = 1 :=
@@ -1556,7 +1556,7 @@ theorem leadingCoeff_divByMonic_of_monic {R : Type u} [CommRing R] {p q : 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))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Ne.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{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))))) -> (forall (a : R), Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.divByMonic.{u1} R (CommRing.toRing.{u1} R _inst_1) p (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)))) (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))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Ne.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{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))))) -> (forall (a : R), Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.divByMonic.{u1} R (CommRing.toRing.{u1} R _inst_1) p (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)))) (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))] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), (Ne.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{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))))) -> (forall (a : R), Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.divByMonic.{u1} R (CommRing.toRing.{u1} R _inst_1) p (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)))) (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_div_by_monic_X_sub_C Polynomial.leadingCoeff_divByMonic_X_sub_Cₓ'. -/
 theorem leadingCoeff_divByMonic_X_sub_C (p : R[X]) (hp : degree p ≠ 0) (a : R) :
     leadingCoeff (p /ₘ (X - C a)) = leadingCoeff p :=
@@ -1572,7 +1572,7 @@ theorem leadingCoeff_divByMonic_X_sub_C (p : R[X]) (hp : degree p ≠ 0) (a : R)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) p) -> (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.commRing.{u1} R _inst_3))))))) p q) -> (LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) q) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) p)) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) q (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) q)) p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) p) -> (Dvd.dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.commRing.{u1} R _inst_3))))))) p q) -> (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) q) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) p)) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) q (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) q)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) q)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) q)) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) 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_3))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) q)) p))
+  forall {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))}, (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) p) -> (Dvd.dvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (semigroupDvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.commRing.{u1} R _inst_3))))))) p q) -> (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) q) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) p)) -> (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) q (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) q)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) q)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) q)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) 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_3))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) q)) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_leading_coeff_mul_of_monic_of_dvd_of_nat_degree_le Polynomial.eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_leₓ'. -/
 theorem eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le {R} [CommRing R] {p q : R[X]}
     (hp : p.Monic) (hdiv : p ∣ q) (hdeg : q.natDegree ≤ p.natDegree) : q = C q.leadingCoeff * p :=
@@ -1603,7 +1603,7 @@ theorem eq_of_monic_of_dvd_of_natDegree_le {R} [CommRing R] {p q : R[X]} (hp : p
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {a : R} {b : R}, (IsUnit.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_3)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_3))))))) a b)) -> (IsCoprime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) a)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) b)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {a : R} {b : R}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_3))) a b)) -> (IsCoprime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) 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_3))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) a)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) b) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) 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_3))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) b)))
+  forall {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {a : R} {b : R}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_3))) a b)) -> (IsCoprime.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) 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_3))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) a)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) b) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) 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_3))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) b)))
 Case conversion may be inaccurate. Consider using '#align polynomial.is_coprime_X_sub_C_of_is_unit_sub Polynomial.isCoprime_X_sub_C_of_isUnit_subₓ'. -/
 theorem isCoprime_X_sub_C_of_isUnit_sub {R} [CommRing R] {a b : R} (h : IsUnit (a - b)) :
     IsCoprime (X - C a) (X - C b) :=
@@ -1629,7 +1629,7 @@ theorem pairwise_coprime_X_sub_C {K} [Field K] {I : Type v} {s : I → K} (H : F
 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))] {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)) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (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))] {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)) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (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))] {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)) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.monic_prod_multiset_X_sub_C Polynomial.monic_prod_multiset_X_sub_Cₓ'. -/
 theorem monic_prod_multiset_X_sub_C : Monic (p.roots.map fun a => X - C a).Prod :=
   monic_multiset_prod_of_monic _ _ fun a _ => monic_X_sub_C a
@@ -1639,7 +1639,7 @@ theorem monic_prod_multiset_X_sub_C : Monic (p.roots.map fun a => X - C a).Prod
 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))] {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))) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))) (Finset.prod.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.toFinset.{u1} R (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (fun (a : R) => HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (Polynomial.rootMultiplicity.{u1} R _inst_1 a 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))] {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))) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))) (Finset.prod.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.toFinset.{u1} R (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (fun (a : R) => HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (Polynomial.rootMultiplicity.{u1} R _inst_1 a 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))] {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))) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))) (Finset.prod.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.toFinset.{u1} R (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (fun (a : R) => HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) (Polynomial.rootMultiplicity.{u1} R _inst_1 a p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.prod_multiset_root_eq_finset_root Polynomial.prod_multiset_root_eq_finset_rootₓ'. -/
 theorem prod_multiset_root_eq_finset_root :
     (p.roots.map fun a => X - C a).Prod =
@@ -1651,7 +1651,7 @@ theorem prod_multiset_root_eq_finset_root :
 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))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 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))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), Dvd.dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 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))] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), Dvd.dvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))) p
 Case conversion may be inaccurate. Consider using '#align polynomial.prod_multiset_X_sub_C_dvd Polynomial.prod_multiset_X_sub_C_dvdₓ'. -/
 /-- The product `∏ (X - a)` for `a` inside the multiset `p.roots` divides `p`. -/
 theorem prod_multiset_X_sub_C_dvd (p : R[X]) : (p.roots.map fun a => X - C a).Prod ∣ p :=
@@ -1668,7 +1668,7 @@ theorem prod_multiset_X_sub_C_dvd (p : R[X]) : (p.roots.map fun a => X - C a).Pr
 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (forall (s : Multiset.{u1} R), Iff (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) s)) p) (LE.le.{u1} (Multiset.{u1} R) (Preorder.toLE.{u1} (Multiset.{u1} R) (PartialOrder.toPreorder.{u1} (Multiset.{u1} R) (Multiset.partialOrder.{u1} R))) s (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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) -> (forall (s : Multiset.{u1} R), Iff (Dvd.dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) s)) p) (LE.le.{u1} (Multiset.{u1} R) (Preorder.toLE.{u1} (Multiset.{u1} R) (PartialOrder.toPreorder.{u1} (Multiset.{u1} R) (Multiset.instPartialOrderMultiset.{u1} R))) s (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))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) -> (forall (s : Multiset.{u1} R), Iff (Dvd.dvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) s)) p) (LE.le.{u1} (Multiset.{u1} R) (Preorder.toLE.{u1} (Multiset.{u1} R) (PartialOrder.toPreorder.{u1} (Multiset.{u1} R) (Multiset.instPartialOrderMultiset.{u1} R))) s (Polynomial.roots.{u1} R _inst_1 _inst_2 p)))
 Case conversion may be inaccurate. Consider using '#align multiset.prod_X_sub_C_dvd_iff_le_roots Multiset.prod_X_sub_C_dvd_iff_le_rootsₓ'. -/
 /-- A Galois connection. -/
 theorem Multiset.prod_X_sub_C_dvd_iff_le_roots {p : R[X]} (hp : p ≠ 0) (s : Multiset R) :
@@ -1687,7 +1687,7 @@ theorem Multiset.prod_X_sub_C_dvd_iff_le_roots {p : R[X]} (hp : p ≠ 0) (s : Mu
 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))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), Exists.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => And (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))) q) p) (And (Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) q)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) (Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 q) (OfNat.ofNat.{u1} (Multiset.{u1} R) 0 (OfNat.mk.{u1} (Multiset.{u1} R) 0 (Zero.zero.{u1} (Multiset.{u1} R) (Multiset.hasZero.{u1} R)))))))
 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))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), Exists.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => And (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))) q) p) (And (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) instAddNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) q)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) (Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 q) (OfNat.ofNat.{u1} (Multiset.{u1} R) 0 (Zero.toOfNat0.{u1} (Multiset.{u1} R) (Multiset.instZeroMultiset.{u1} R))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => And (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (HMul.hMul.{u1, 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))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))) q) p) (And (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) instAddNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) q)) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) (Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 q) (OfNat.ofNat.{u1} (Multiset.{u1} R) 0 (Zero.toOfNat0.{u1} (Multiset.{u1} R) (Multiset.instZeroMultiset.{u1} R))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.exists_prod_multiset_X_sub_C_mul Polynomial.exists_prod_multiset_X_sub_C_mulₓ'. -/
 theorem exists_prod_multiset_X_sub_C_mul (p : R[X]) :
     ∃ q,
@@ -1712,7 +1712,7 @@ theorem exists_prod_multiset_X_sub_C_mul (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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Eq.{1} Nat (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{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))) (HMul.hMul.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (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))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} 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(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))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) (Multiset.prod.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) (CommRing.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 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))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) (Polynomial.mul'.{u1} R 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(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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)))) p)
 Case conversion may be inaccurate. Consider using '#align polynomial.C_leading_coeff_mul_prod_multiset_X_sub_C Polynomial.C_leadingCoeff_mul_prod_multiset_X_sub_Cₓ'. -/
 /-- A polynomial `p` that has as many roots as its degree
 can be written `p = p.leading_coeff * ∏(X - a)`, for `a` in `p.roots`. -/
@@ -1727,7 +1727,7 @@ theorem C_leadingCoeff_mul_prod_multiset_X_sub_C (hroots : p.roots.card = p.natD
 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))] {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.{1} Nat (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{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))) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 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))] {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.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{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))) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 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))] {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.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p)) -> (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))) p)
 Case conversion may be inaccurate. Consider using '#align polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq Polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eqₓ'. -/
 /-- A monic polynomial `p` that has as many roots as its degree
 can be written `p = ∏(X - a)`, for `a` in `p.roots`. -/
@@ -1748,7 +1748,7 @@ variable {A B : Type _} [CommRing A] [CommRing B]
 lean 3 declaration is
   forall {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommRing.{u1} A] [_inst_2 : CommRing.{u2} B] {p : Polynomial.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))} {f : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))}, (Ne.{succ u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p) (OfNat.ofNat.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) 0 (OfNat.mk.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) 0 (Zero.zero.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) (Polynomial.zero.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))))))) -> (forall (a : A), LE.le.{0} Nat Nat.hasLe (Polynomial.rootMultiplicity.{u1} A _inst_1 a p) (Polynomial.rootMultiplicity.{u2} B _inst_2 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f a) (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p)))
 but is expected to have type
-  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] {p : Polynomial.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))} {f : RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))}, (Ne.{succ u1} (Polynomial.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2))) (Polynomial.map.{u2, u1} A B (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1)) (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2)) f p) (OfNat.ofNat.{u1} (Polynomial.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2))) (Polynomial.zero.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2)))))) -> (forall (a : A), LE.le.{0} Nat instLENat (Polynomial.rootMultiplicity.{u2} A _inst_1 a p) (Polynomial.rootMultiplicity.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) _inst_2 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))))) f a) (Polynomial.map.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1)) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) _inst_2)) f p)))
+  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] {p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))} {f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))}, (Ne.{succ u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p) (OfNat.ofNat.{u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (Polynomial.zero.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))))) -> (forall (a : A), LE.le.{0} Nat instLENat (Polynomial.rootMultiplicity.{u2} A _inst_1 a p) (Polynomial.rootMultiplicity.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) _inst_2 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f a) (Polynomial.map.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) _inst_2)) f p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.le_root_multiplicity_map Polynomial.le_rootMultiplicity_mapₓ'. -/
 theorem le_rootMultiplicity_map {p : A[X]} {f : A →+* B} (hmap : map f p ≠ 0) (a : A) :
     rootMultiplicity a p ≤ rootMultiplicity (f a) (p.map f) :=
@@ -1762,7 +1762,7 @@ theorem le_rootMultiplicity_map {p : A[X]} {f : A →+* B} (hmap : map f p ≠ 0
 lean 3 declaration is
   forall {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommRing.{u1} A] [_inst_2 : CommRing.{u2} B] {p : Polynomial.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))} {f : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))}, (Function.Injective.{succ u1, succ u2} A B (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f)) -> (forall (a : A), Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} A _inst_1 a p) (Polynomial.rootMultiplicity.{u2} B _inst_2 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f a) (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p)))
 but is expected to have type
-  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] {p : Polynomial.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))} {f : RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))))) f)) -> (forall (a : A), Eq.{1} Nat (Polynomial.rootMultiplicity.{u2} A _inst_1 a p) (Polynomial.rootMultiplicity.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) _inst_2 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))))) f a) (Polynomial.map.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1)) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) _inst_2)) f p)))
+  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] {p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))} {f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f)) -> (forall (a : A), Eq.{1} Nat (Polynomial.rootMultiplicity.{u2} A _inst_1 a p) (Polynomial.rootMultiplicity.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) _inst_2 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f a) (Polynomial.map.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) _inst_2)) f p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_root_multiplicity_map Polynomial.eq_rootMultiplicity_mapₓ'. -/
 theorem eq_rootMultiplicity_map {p : A[X]} {f : A →+* B} (hf : Function.Injective f) (a : A) :
     rootMultiplicity a p = rootMultiplicity (f a) (p.map f) :=
@@ -1778,7 +1778,7 @@ theorem eq_rootMultiplicity_map {p : A[X]} {f : A →+* B} (hf : Function.Inject
 lean 3 declaration is
   forall {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommRing.{u1} A] [_inst_2 : CommRing.{u2} B] [_inst_3 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))] {p : Polynomial.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))} {f : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))}, (Ne.{succ u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p) (OfNat.ofNat.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) 0 (OfNat.mk.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) 0 (Zero.zero.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) (Polynomial.zero.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))))))) -> (forall (b : B), LE.le.{0} Nat Nat.hasLe (Multiset.count.{u2} B (fun (a : B) (b : B) => Classical.propDecidable (Eq.{succ u2} B a b)) b (Multiset.map.{u1, u2} A B (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f) (Polynomial.roots.{u1} A _inst_1 _inst_3 p))) (Polynomial.rootMultiplicity.{u2} B _inst_2 b (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p)))
 but is expected to have type
-  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_3 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))] {p : Polynomial.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))} {f : RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))}, (Ne.{succ u1} (Polynomial.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2))) (Polynomial.map.{u2, u1} A B (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1)) (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2)) f p) (OfNat.ofNat.{u1} (Polynomial.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2))) (Polynomial.zero.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2)))))) -> (forall (b : B), LE.le.{0} Nat instLENat (Multiset.count.{u1} B (fun (a : B) (b : B) => Classical.propDecidable (Eq.{succ u1} B a b)) b (Multiset.map.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))))) f) (Polynomial.roots.{u2} A _inst_1 _inst_3 p))) (Polynomial.rootMultiplicity.{u1} B _inst_2 b (Polynomial.map.{u2, u1} A B (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1)) (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2)) f p)))
+  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))] {p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))} {f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))}, (Ne.{succ u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p) (OfNat.ofNat.{u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (Polynomial.zero.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))))) -> (forall (b : B), LE.le.{0} Nat instLENat (Multiset.count.{u1} B (fun (a : B) (b : B) => Classical.propDecidable (Eq.{succ u1} B a b)) b (Multiset.map.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f) (Polynomial.roots.{u2} A _inst_1 _inst_3 p))) (Polynomial.rootMultiplicity.{u1} B _inst_2 b (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.count_map_roots Polynomial.count_map_rootsₓ'. -/
 theorem count_map_roots [IsDomain A] {p : A[X]} {f : A →+* B} (hmap : map f p ≠ 0) (b : B) :
     (p.roots.map f).count b ≤ rootMultiplicity b (p.map f) :=
@@ -1797,7 +1797,7 @@ theorem count_map_roots [IsDomain A] {p : A[X]} {f : A →+* B} (hmap : map f p
 lean 3 declaration is
   forall {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommRing.{u1} A] [_inst_2 : CommRing.{u2} B] [_inst_3 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))] (p : Polynomial.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))) {f : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))}, (Function.Injective.{succ u1, succ u2} A B (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f)) -> (forall (b : B), LE.le.{0} Nat Nat.hasLe (Multiset.count.{u2} B (fun (a : B) (b : B) => Classical.propDecidable (Eq.{succ u2} B a b)) b (Multiset.map.{u1, u2} A B (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f) (Polynomial.roots.{u1} A _inst_1 _inst_3 p))) (Polynomial.rootMultiplicity.{u2} B _inst_2 b (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p)))
 but is expected to have type
-  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_3 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))] (p : Polynomial.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))) {f : RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))))) f)) -> (forall (b : B), LE.le.{0} Nat instLENat (Multiset.count.{u1} B (fun (a : B) (b : B) => Classical.propDecidable (Eq.{succ u1} B a b)) b (Multiset.map.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))))) f) (Polynomial.roots.{u2} A _inst_1 _inst_3 p))) (Polynomial.rootMultiplicity.{u1} B _inst_2 b (Polynomial.map.{u2, u1} A B (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1)) (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2)) f p)))
+  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))] (p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) {f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f)) -> (forall (b : B), LE.le.{0} Nat instLENat (Multiset.count.{u1} B (fun (a : B) (b : B) => Classical.propDecidable (Eq.{succ u1} B a b)) b (Multiset.map.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f) (Polynomial.roots.{u2} A _inst_1 _inst_3 p))) (Polynomial.rootMultiplicity.{u1} B _inst_2 b (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.count_map_roots_of_injective Polynomial.count_map_roots_of_injectiveₓ'. -/
 theorem count_map_roots_of_injective [IsDomain A] (p : A[X]) {f : A →+* B}
     (hf : Function.Injective f) (b : B) : (p.roots.map f).count b ≤ rootMultiplicity b (p.map f) :=
@@ -1813,7 +1813,7 @@ theorem count_map_roots_of_injective [IsDomain A] (p : A[X]) {f : A →+* B}
 lean 3 declaration is
   forall {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommRing.{u1} A] [_inst_2 : CommRing.{u2} B] [_inst_3 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))] [_inst_4 : IsDomain.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))] {p : Polynomial.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))} {f : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))}, (Ne.{succ u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p) (OfNat.ofNat.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) 0 (OfNat.mk.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) 0 (Zero.zero.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) (Polynomial.zero.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))))))) -> (LE.le.{u2} (Multiset.{u2} B) (Preorder.toLE.{u2} (Multiset.{u2} B) (PartialOrder.toPreorder.{u2} (Multiset.{u2} B) (Multiset.partialOrder.{u2} B))) (Multiset.map.{u1, u2} A B (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f) (Polynomial.roots.{u1} A _inst_1 _inst_3 p)) (Polynomial.roots.{u2} B _inst_2 _inst_4 (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p)))
 but is expected to have type
-  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_3 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))] [_inst_4 : IsDomain.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2))] {p : Polynomial.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))} {f : RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))}, (Ne.{succ u1} (Polynomial.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2))) (Polynomial.map.{u2, u1} A B (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1)) (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2)) f p) (OfNat.ofNat.{u1} (Polynomial.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2))) (Polynomial.zero.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2)))))) -> (LE.le.{u1} (Multiset.{u1} B) (Preorder.toLE.{u1} (Multiset.{u1} B) (PartialOrder.toPreorder.{u1} (Multiset.{u1} B) (Multiset.instPartialOrderMultiset.{u1} B))) (Multiset.map.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))))) f) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (Polynomial.roots.{u1} B _inst_2 _inst_4 (Polynomial.map.{u2, u1} A B (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1)) (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2)) f p)))
+  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))] [_inst_4 : IsDomain.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))] {p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))} {f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))}, (Ne.{succ u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p) (OfNat.ofNat.{u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (Polynomial.zero.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))))) -> (LE.le.{u1} (Multiset.{u1} B) (Preorder.toLE.{u1} (Multiset.{u1} B) (PartialOrder.toPreorder.{u1} (Multiset.{u1} B) (Multiset.instPartialOrderMultiset.{u1} B))) (Multiset.map.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (Polynomial.roots.{u1} B _inst_2 _inst_4 (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_roots_le Polynomial.map_roots_leₓ'. -/
 theorem map_roots_le [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (h : p.map f ≠ 0) :
     p.roots.map f ≤ (p.map f).roots :=
@@ -1826,7 +1826,7 @@ theorem map_roots_le [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (h : p
 lean 3 declaration is
   forall {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommRing.{u1} A] [_inst_2 : CommRing.{u2} B] [_inst_3 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))] [_inst_4 : IsDomain.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))] (p : Polynomial.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))) {f : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))}, (Function.Injective.{succ u1, succ u2} A B (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f)) -> (LE.le.{u2} (Multiset.{u2} B) (Preorder.toLE.{u2} (Multiset.{u2} B) (PartialOrder.toPreorder.{u2} (Multiset.{u2} B) (Multiset.partialOrder.{u2} B))) (Multiset.map.{u1, u2} A B (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f) (Polynomial.roots.{u1} A _inst_1 _inst_3 p)) (Polynomial.roots.{u2} B _inst_2 _inst_4 (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p)))
 but is expected to have type
-  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_3 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))] [_inst_4 : IsDomain.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2))] (p : Polynomial.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))) {f : RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))))) f)) -> (LE.le.{u1} (Multiset.{u1} B) (Preorder.toLE.{u1} (Multiset.{u1} B) (PartialOrder.toPreorder.{u1} (Multiset.{u1} B) (Multiset.instPartialOrderMultiset.{u1} B))) (Multiset.map.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))))) f) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (Polynomial.roots.{u1} B _inst_2 _inst_4 (Polynomial.map.{u2, u1} A B (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1)) (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2)) f p)))
+  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))] [_inst_4 : IsDomain.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))] (p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) {f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f)) -> (LE.le.{u1} (Multiset.{u1} B) (Preorder.toLE.{u1} (Multiset.{u1} B) (PartialOrder.toPreorder.{u1} (Multiset.{u1} B) (Multiset.instPartialOrderMultiset.{u1} B))) (Multiset.map.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (Polynomial.roots.{u1} B _inst_2 _inst_4 (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_roots_le_of_injective Polynomial.map_roots_le_of_injectiveₓ'. -/
 theorem map_roots_le_of_injective [IsDomain A] [IsDomain B] (p : A[X]) {f : A →+* B}
     (hf : Function.Injective f) : p.roots.map f ≤ (p.map f).roots :=
@@ -1839,7 +1839,7 @@ theorem map_roots_le_of_injective [IsDomain A] [IsDomain B] (p : A[X]) {f : A 
 lean 3 declaration is
   forall {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommRing.{u1} A] [_inst_2 : CommRing.{u2} B] [_inst_3 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))] [_inst_4 : IsDomain.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))] {p : Polynomial.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))} {f : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))}, (Ne.{succ u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p) (OfNat.ofNat.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) 0 (OfNat.mk.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) 0 (Zero.zero.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) (Polynomial.zero.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))))))) -> (LE.le.{0} Nat Nat.hasLe (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} A) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} A) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} A) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} A) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} A) (Multiset.orderedCancelAddCommMonoid.{u1} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} A) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} A) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} A) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} A) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} A) (Multiset.orderedCancelAddCommMonoid.{u1} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} A) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} A) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} A) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} A) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} A) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} A) (Multiset.orderedCancelAddCommMonoid.{u1} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} A) (Polynomial.roots.{u1} A _inst_1 _inst_3 p)) (coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} (Multiset.{u2} B) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} B) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} B) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} B) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} B) (Multiset.orderedCancelAddCommMonoid.{u2} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} (Multiset.{u2} B) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} B) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} B) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} B) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} B) (Multiset.orderedCancelAddCommMonoid.{u2} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u2} B) -> Nat) (AddMonoidHom.hasCoeToFun.{u2, 0} (Multiset.{u2} B) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} B) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} B) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} B) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} B) (Multiset.orderedCancelAddCommMonoid.{u2} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u2} B) (Polynomial.roots.{u2} B _inst_2 _inst_4 (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p))))
 but is expected to have type
-  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_3 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))] [_inst_4 : IsDomain.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2))] {p : Polynomial.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))} {f : RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))}, (Ne.{succ u1} (Polynomial.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2))) (Polynomial.map.{u2, u1} A B (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1)) (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2)) f p) (OfNat.ofNat.{u1} (Polynomial.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2))) (Polynomial.zero.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2)))))) -> (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} A) => Nat) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) instLENat (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) (fun (_x : Multiset.{u2} A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} A) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} A) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} A) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} B) (fun (_x : Multiset.{u1} B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} B) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} B) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} B) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} B) (Polynomial.roots.{u1} B _inst_2 _inst_4 (Polynomial.map.{u2, u1} A B (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1)) (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2)) f p))))
+  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))] [_inst_4 : IsDomain.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))] {p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))} {f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))}, (Ne.{succ u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p) (OfNat.ofNat.{u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (Polynomial.zero.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))))) -> (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} A) => Nat) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) instLENat (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) (fun (_x : Multiset.{u2} A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} A) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} A) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} A) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} B) (fun (_x : Multiset.{u1} B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} B) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} B) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} B) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} B) (Polynomial.roots.{u1} B _inst_2 _inst_4 (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p))))
 Case conversion may be inaccurate. Consider using '#align polynomial.card_roots_le_map Polynomial.card_roots_le_mapₓ'. -/
 theorem card_roots_le_map [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (h : p.map f ≠ 0) :
     p.roots.card ≤ (p.map f).roots.card :=
@@ -1852,7 +1852,7 @@ theorem card_roots_le_map [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (
 lean 3 declaration is
   forall {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommRing.{u1} A] [_inst_2 : CommRing.{u2} B] [_inst_3 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))] [_inst_4 : IsDomain.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))] {p : Polynomial.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))} {f : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))}, (Function.Injective.{succ u1, succ u2} A B (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f)) -> (LE.le.{0} Nat Nat.hasLe (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} A) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} A) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} A) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} A) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} A) (Multiset.orderedCancelAddCommMonoid.{u1} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} A) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} A) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} A) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} A) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} A) (Multiset.orderedCancelAddCommMonoid.{u1} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} A) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} A) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} A) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} A) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} A) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} A) (Multiset.orderedCancelAddCommMonoid.{u1} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} A) (Polynomial.roots.{u1} A _inst_1 _inst_3 p)) (coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} (Multiset.{u2} B) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} B) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} B) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} B) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} B) (Multiset.orderedCancelAddCommMonoid.{u2} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} (Multiset.{u2} B) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} B) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} B) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} B) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} B) (Multiset.orderedCancelAddCommMonoid.{u2} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u2} B) -> Nat) (AddMonoidHom.hasCoeToFun.{u2, 0} (Multiset.{u2} B) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} B) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} B) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} B) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} B) (Multiset.orderedCancelAddCommMonoid.{u2} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u2} B) (Polynomial.roots.{u2} B _inst_2 _inst_4 (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p))))
 but is expected to have type
-  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_3 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))] [_inst_4 : IsDomain.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2))] {p : Polynomial.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))} {f : RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))))) f)) -> (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} A) => Nat) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) instLENat (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) (fun (_x : Multiset.{u2} A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} A) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} A) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} A) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} B) (fun (_x : Multiset.{u1} B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} B) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} B) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} B) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} B) (Polynomial.roots.{u1} B _inst_2 _inst_4 (Polynomial.map.{u2, u1} A B (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1)) (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2)) f p))))
+  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))] [_inst_4 : IsDomain.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))] {p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))} {f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f)) -> (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} A) => Nat) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) instLENat (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) (fun (_x : Multiset.{u2} A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} A) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} A) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} A) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} B) (fun (_x : Multiset.{u1} B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} B) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} B) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} B) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} B) (Polynomial.roots.{u1} B _inst_2 _inst_4 (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p))))
 Case conversion may be inaccurate. Consider using '#align polynomial.card_roots_le_map_of_injective Polynomial.card_roots_le_map_of_injectiveₓ'. -/
 theorem card_roots_le_map_of_injective [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B}
     (hf : Function.Injective f) : p.roots.card ≤ (p.map f).roots.card :=
@@ -1865,7 +1865,7 @@ theorem card_roots_le_map_of_injective [IsDomain A] [IsDomain B] {p : A[X]} {f :
 lean 3 declaration is
   forall {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommRing.{u1} A] [_inst_2 : CommRing.{u2} B] [_inst_3 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))] [_inst_4 : IsDomain.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))] {p : Polynomial.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))} {f : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))}, (Function.Injective.{succ u1, succ u2} A B (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f)) -> (Eq.{1} Nat (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} A) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} A) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} A) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} A) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} A) (Multiset.orderedCancelAddCommMonoid.{u1} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} A) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} A) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} A) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} A) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} A) (Multiset.orderedCancelAddCommMonoid.{u1} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} A) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} A) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} A) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} A) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} A) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} A) (Multiset.orderedCancelAddCommMonoid.{u1} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} A) (Polynomial.roots.{u1} A _inst_1 _inst_3 p)) (Polynomial.natDegree.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) p)) -> (Eq.{succ u2} (Multiset.{u2} B) (Multiset.map.{u1, u2} A B (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f) (Polynomial.roots.{u1} A _inst_1 _inst_3 p)) (Polynomial.roots.{u2} B _inst_2 _inst_4 (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p)))
 but is expected to have type
-  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_3 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))] [_inst_4 : IsDomain.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2))] {p : Polynomial.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))} {f : RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))))) f)) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} A) => Nat) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) (fun (_x : Multiset.{u2} A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} A) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} A) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} A) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (Polynomial.natDegree.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1)) p)) -> (Eq.{succ u1} (Multiset.{u1} B) (Multiset.map.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))))) f) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (Polynomial.roots.{u1} B _inst_2 _inst_4 (Polynomial.map.{u2, u1} A B (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1)) (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2)) f p)))
+  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_3 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))] [_inst_4 : IsDomain.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))] {p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))} {f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f)) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} A) => Nat) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) (fun (_x : Multiset.{u2} A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} A) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} A) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} A) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (Polynomial.natDegree.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) p)) -> (Eq.{succ u1} (Multiset.{u1} B) (Multiset.map.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (Polynomial.roots.{u1} B _inst_2 _inst_4 (Polynomial.map.{u2, u1} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) f p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_map_of_injective_of_card_eq_nat_degree Polynomial.roots_map_of_injective_of_card_eq_natDegreeₓ'. -/
 theorem roots_map_of_injective_of_card_eq_natDegree [IsDomain A] [IsDomain B] {p : A[X]}
     {f : A →+* B} (hf : Function.Injective f) (hroots : p.roots.card = p.natDegree) :
@@ -1885,7 +1885,7 @@ variable [Semiring R] [CommRing S] [IsDomain S] (φ : R →+* S)
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (φ : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) {f : Polynomial.{u1} R _inst_1}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) -> (IsUnit.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ring.toMonoid.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Polynomial.ring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Polynomial.map.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) φ f)) -> (IsUnit.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) f)
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (φ : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) {f : Polynomial.{u1} R _inst_1}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) -> (IsUnit.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (MonoidWithZero.toMonoid.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Semiring.toMonoidWithZero.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Polynomial.semiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Polynomial.map.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) φ f)) -> (IsUnit.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) f)
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] (φ : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) {f : Polynomial.{u1} R _inst_1}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) -> (IsUnit.{u2} (Polynomial.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (MonoidWithZero.toMonoid.{u2} (Polynomial.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Semiring.toMonoidWithZero.{u2} (Polynomial.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Polynomial.semiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Polynomial.map.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) φ f)) -> (IsUnit.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) f)
 Case conversion may be inaccurate. Consider using '#align polynomial.is_unit_of_is_unit_leading_coeff_of_is_unit_map Polynomial.isUnit_of_isUnit_leadingCoeff_of_isUnit_mapₓ'. -/
 theorem isUnit_of_isUnit_leadingCoeff_of_isUnit_map {f : R[X]} (hf : IsUnit f.leadingCoeff)
     (H : IsUnit (map φ f)) : IsUnit f :=
@@ -1914,7 +1914,7 @@ variable [CommRing R] [IsDomain R] [CommRing S] [IsDomain S] (φ : R →+* S)
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : CommRing.{u2} S] [_inst_4 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3))] (φ : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_3)))) (f : 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)) f) -> (Irreducible.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3))) (Ring.toMonoid.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3))) (Polynomial.ring.{u2} S (CommRing.toRing.{u2} S _inst_3))) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3)) φ f)) -> (Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : CommRing.{u2} S] [_inst_4 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3))] (φ : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_3)))) (f : 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)) f) -> (Irreducible.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3))) (MonoidWithZero.toMonoid.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3))) (Semiring.toMonoidWithZero.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3))) (Polynomial.semiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3))))) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3)) φ f)) -> (Irreducible.{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))) (Semiring.toMonoidWithZero.{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))))) f)
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : CommRing.{u2} S] [_inst_4 : IsDomain.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_3))] (φ : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_3)))) (f : 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)) f) -> (Irreducible.{u2} (Polynomial.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_3))) (MonoidWithZero.toMonoid.{u2} (Polynomial.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_3))) (Semiring.toMonoidWithZero.{u2} (Polynomial.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_3))) (Polynomial.semiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_3))))) (Polynomial.map.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_3)) φ f)) -> (Irreducible.{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))) (Semiring.toMonoidWithZero.{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))))) f)
 Case conversion may be inaccurate. Consider using '#align polynomial.monic.irreducible_of_irreducible_map Polynomial.Monic.irreducible_of_irreducible_mapₓ'. -/
 /-- A polynomial over an integral domain `R` is irreducible if it is monic and
   irreducible after mapping into an integral domain `S`.

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

@@ -1708,20 +1708,20 @@ theorem exists_prod_multiset_X_sub_C_mul (p : R[X]) :
     exacts[add_right_eq_self.1 he, mul_ne_zero monic_prod_multiset_X_sub_C.ne_zero hq]
 #align polynomial.exists_prod_multiset_X_sub_C_mul Polynomial.exists_prod_multiset_X_sub_C_mul
 
-/- warning: polynomial.C_leading_coeff_mul_prod_multiset_X_sub_C -> Polynomial.c_leadingCoeff_mul_prod_multiset_X_sub_C is a dubious translation:
+/- warning: polynomial.C_leading_coeff_mul_prod_multiset_X_sub_C -> Polynomial.C_leadingCoeff_mul_prod_multiset_X_sub_C 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Eq.{1} Nat (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{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))) (HMul.hMul.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (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))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, 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-Case conversion may be inaccurate. Consider using '#align polynomial.C_leading_coeff_mul_prod_multiset_X_sub_C Polynomial.c_leadingCoeff_mul_prod_multiset_X_sub_Cₓ'. -/
+Case conversion may be inaccurate. Consider using '#align polynomial.C_leading_coeff_mul_prod_multiset_X_sub_C Polynomial.C_leadingCoeff_mul_prod_multiset_X_sub_Cₓ'. -/
 /-- A polynomial `p` that has as many roots as its degree
 can be written `p = p.leading_coeff * ∏(X - a)`, for `a` in `p.roots`. -/
-theorem c_leadingCoeff_mul_prod_multiset_X_sub_C (hroots : p.roots.card = p.natDegree) :
+theorem C_leadingCoeff_mul_prod_multiset_X_sub_C (hroots : p.roots.card = p.natDegree) :
     C p.leadingCoeff * (p.roots.map fun a => X - C a).Prod = p :=
   (eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le monic_prod_multiset_X_sub_C
       p.prod_multiset_X_sub_C_dvd
       ((natDegree_multiset_prod_X_sub_C_eq_card _).trans hroots).ge).symm
-#align polynomial.C_leading_coeff_mul_prod_multiset_X_sub_C Polynomial.c_leadingCoeff_mul_prod_multiset_X_sub_C
+#align polynomial.C_leading_coeff_mul_prod_multiset_X_sub_C Polynomial.C_leadingCoeff_mul_prod_multiset_X_sub_C
 
 /- warning: polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq -> Polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq is a dubious translation:
 lean 3 declaration is

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

@@ -1212,7 +1212,7 @@ def nthRootsFinset (n : ℕ) (R : Type _) [CommRing R] [IsDomain R] : Finset R :
 
 /- warning: polynomial.mem_nth_roots_finset -> Polynomial.mem_nthRootsFinset 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))] {n : Nat}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n) -> (forall {x : R}, Iff (Membership.Mem.{u1, u1} R (Finset.{u1} R) (Finset.hasMem.{u1} R) x (Polynomial.nthRootsFinset.{u1} n R _inst_1 _inst_2)) (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) x n) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {n : Nat}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n) -> (forall {x : R}, Iff (Membership.Mem.{u1, u1} R (Finset.{u1} R) (Finset.hasMem.{u1} R) x (Polynomial.nthRootsFinset.{u1} n R _inst_1 _inst_2)) (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) x n) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))
 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))] {n : Nat}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) -> (forall {x : R}, Iff (Membership.mem.{u1, u1} R (Finset.{u1} R) (Finset.instMembershipFinset.{u1} R) x (Polynomial.nthRootsFinset.{u1} n R _inst_1 _inst_2)) (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) x n) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.mem_nth_roots_finset Polynomial.mem_nthRootsFinsetₓ'. -/
@@ -1601,7 +1601,7 @@ theorem eq_of_monic_of_dvd_of_natDegree_le {R} [CommRing R] {p q : R[X]} (hp : p
 
 /- warning: polynomial.is_coprime_X_sub_C_of_is_unit_sub -> Polynomial.isCoprime_X_sub_C_of_isUnit_sub is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {a : R} {b : R}, (IsUnit.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_3)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))))) a b)) -> (IsCoprime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) a)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) b)))
+  forall {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {a : R} {b : R}, (IsUnit.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_3)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_3))))))) a b)) -> (IsCoprime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) a)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) b)))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {a : R} {b : R}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_3))) a b)) -> (IsCoprime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) 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_3))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) a)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) b) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R 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_inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) b)))
 Case conversion may be inaccurate. Consider using '#align polynomial.is_coprime_X_sub_C_of_is_unit_sub Polynomial.isCoprime_X_sub_C_of_isUnit_subₓ'. -/

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, Johan Commelin
 
 ! This file was ported from Lean 3 source module data.polynomial.ring_division
-! leanprover-community/mathlib commit 97eab48559068f3d6313da387714ef25768fb730
+! leanprover-community/mathlib commit 517cc149e0b515d2893baa376226ed10feb319c7
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1179,7 +1179,7 @@ Case conversion may be inaccurate. Consider using '#align polynomial.card_nth_ro
 theorem card_nthRoots (n : ℕ) (a : R) : (nthRoots n a).card ≤ n :=
   if hn : n = 0 then
     if h : (X : R[X]) ^ n - C a = 0 then by
-      simp only [Nat.zero_le, nth_roots, roots, h, dif_pos rfl, empty_eq_zero, card_zero]
+      simp only [Nat.zero_le, nth_roots, roots, h, dif_pos rfl, empty_eq_zero, Multiset.card_zero]
     else
       WithBot.coe_le_coe.1
         (le_trans (card_roots h)

mathlib commit https://github.com/leanprover-community/mathlib/commit/d11893b411025250c8e61ff2f12ccbd7ee35ab15

@@ -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, Johan Commelin
 
 ! This file was ported from Lean 3 source module data.polynomial.ring_division
-! leanprover-community/mathlib commit cbdf7b565832144d024caa5a550117c6df0204a5
+! leanprover-community/mathlib commit 97eab48559068f3d6313da387714ef25768fb730
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -18,6 +18,9 @@ import Mathbin.Algebra.Polynomial.BigOperators
 /-!
 # 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] $
 
 ## Main definitions

mathlib commit https://github.com/leanprover-community/mathlib/commit/57e09a1296bfb4330ddf6624f1028ba186117d82

@@ -55,16 +55,21 @@ section
 
 variable [Semiring S]
 
+#print Polynomial.natDegree_pos_of_aeval_root /-
 theorem natDegree_pos_of_aeval_root [Algebra R S] {p : R[X]} (hp : p ≠ 0) {z : S}
     (hz : aeval z p = 0) (inj : ∀ x : R, algebraMap R S x = 0 → x = 0) : 0 < p.natDegree :=
   natDegree_pos_of_eval₂_root hp (algebraMap R S) hz inj
 #align polynomial.nat_degree_pos_of_aeval_root Polynomial.natDegree_pos_of_aeval_root
+-/
 
+#print Polynomial.degree_pos_of_aeval_root /-
 theorem degree_pos_of_aeval_root [Algebra R S] {p : R[X]} (hp : p ≠ 0) {z : S} (hz : aeval z p = 0)
     (inj : ∀ x : R, algebraMap R S x = 0 → x = 0) : 0 < p.degree :=
   natDegree_pos_iff_degree_pos.mp (natDegree_pos_of_aeval_root hp hz inj)
 #align polynomial.degree_pos_of_aeval_root Polynomial.degree_pos_of_aeval_root
+-/
 
+#print Polynomial.modByMonic_eq_of_dvd_sub /-
 theorem modByMonic_eq_of_dvd_sub (hq : q.Monic) {p₁ p₂ : R[X]} (h : q ∣ p₁ - p₂) :
     p₁ %ₘ q = p₂ %ₘ q := by
   nontriviality R
@@ -72,7 +77,9 @@ theorem modByMonic_eq_of_dvd_sub (hq : q.Monic) {p₁ p₂ : R[X]} (h : q ∣ p
   refine' (div_mod_by_monic_unique (p₂ /ₘ q + f) _ hq ⟨_, degree_mod_by_monic_lt _ hq⟩).2
   rw [sub_eq_iff_eq_add.mp sub_eq, mul_add, ← add_assoc, mod_by_monic_add_div _ hq, add_comm]
 #align polynomial.mod_by_monic_eq_of_dvd_sub Polynomial.modByMonic_eq_of_dvd_sub
+-/
 
+#print Polynomial.add_modByMonic /-
 theorem add_modByMonic (p₁ p₂ : R[X]) : (p₁ + p₂) %ₘ q = p₁ %ₘ q + p₂ %ₘ q :=
   by
   by_cases hq : q.monic
@@ -86,7 +93,9 @@ theorem add_modByMonic (p₁ p₂ : R[X]) : (p₁ + p₂) %ₘ q = p₁ %ₘ q +
               (max_lt (degree_mod_by_monic_lt _ hq) (degree_mod_by_monic_lt _ hq))⟩).2
   · simp_rw [mod_by_monic_eq_of_not_monic _ hq]
 #align polynomial.add_mod_by_monic Polynomial.add_modByMonic
+-/
 
+#print Polynomial.smul_modByMonic /-
 theorem smul_modByMonic (c : R) (p : R[X]) : c • p %ₘ q = c • (p %ₘ q) :=
   by
   by_cases hq : q.monic
@@ -97,7 +106,9 @@ theorem smul_modByMonic (c : R) (p : R[X]) : c • p %ₘ q = c • (p %ₘ q) :
             (degree_smul_le _ _).trans_lt (degree_mod_by_monic_lt _ hq)⟩).2
   · simp_rw [mod_by_monic_eq_of_not_monic _ hq]
 #align polynomial.smul_mod_by_monic Polynomial.smul_modByMonic
+-/
 
+#print Polynomial.modByMonicHom /-
 /-- `_ %ₘ q` as an `R`-linear map. -/
 @[simps]
 def modByMonicHom (q : R[X]) : R[X] →ₗ[R] R[X]
@@ -106,6 +117,7 @@ def modByMonicHom (q : R[X]) : R[X] →ₗ[R] R[X]
   map_add' := add_modByMonic
   map_smul' := smul_modByMonic
 #align polynomial.mod_by_monic_hom Polynomial.modByMonicHom
+-/
 
 end
 
@@ -113,12 +125,14 @@ section
 
 variable [Ring S]
 
+#print Polynomial.aeval_modByMonic_eq_self_of_root /-
 theorem aeval_modByMonic_eq_self_of_root [Algebra R S] {p q : R[X]} (hq : q.Monic) {x : S}
     (hx : aeval x q = 0) : aeval x (p %ₘ q) = aeval x p :=
   by-- `eval₂_mod_by_monic_eq_self_of_root` doesn't work here as it needs commutativity
   rw [mod_by_monic_eq_sub_mul_div p hq, _root_.map_sub, _root_.map_mul, hx, MulZeroClass.zero_mul,
     sub_zero]
 #align polynomial.aeval_mod_by_monic_eq_self_of_root Polynomial.aeval_modByMonic_eq_self_of_root
+-/
 
 end
 
@@ -135,12 +149,24 @@ instance : NoZeroDivisors R[X]
     refine' eq_zero_or_eq_zero_of_mul_eq_zero _
     rw [← leading_coeff_zero, ← leading_coeff_mul, h]
 
+/- warning: polynomial.nat_degree_mul -> Polynomial.natDegree_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))) -> (Ne.{succ u1} (Polynomial.{u1} R _inst_1) q (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p q)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Polynomial.natDegree.{u1} R _inst_1 p) (Polynomial.natDegree.{u1} R _inst_1 q)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))) -> (Ne.{succ u1} (Polynomial.{u1} R _inst_1) q (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p q)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Polynomial.natDegree.{u1} R _inst_1 p) (Polynomial.natDegree.{u1} R _inst_1 q)))
+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_mul Polynomial.natDegree_mulₓ'. -/
 theorem natDegree_mul (hp : p ≠ 0) (hq : q ≠ 0) : natDegree (p * q) = natDegree p + natDegree q :=
   by
   rw [← WithBot.coe_eq_coe, ← degree_eq_nat_degree (mul_ne_zero hp hq), WithBot.coe_add, ←
     degree_eq_nat_degree hp, ← degree_eq_nat_degree hq, degree_mul]
 #align polynomial.nat_degree_mul Polynomial.natDegree_mul
 
+/- warning: polynomial.trailing_degree_mul -> Polynomial.trailingDegree_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, Eq.{1} ENat (Polynomial.trailingDegree.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) p q)) (HAdd.hAdd.{0, 0, 0} ENat ENat ENat (instHAdd.{0} ENat (Distrib.toHasAdd.{0} ENat (NonUnitalNonAssocSemiring.toDistrib.{0} ENat (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENat (Semiring.toNonAssocSemiring.{0} ENat (OrderedSemiring.toSemiring.{0} ENat (OrderedCommSemiring.toOrderedSemiring.{0} ENat (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENat ENat.canonicallyOrderedCommSemiring)))))))) (Polynomial.trailingDegree.{u1} R _inst_1 p) (Polynomial.trailingDegree.{u1} R _inst_1 q))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.trailing_degree_mul Polynomial.trailingDegree_mulₓ'. -/
 theorem trailingDegree_mul : (p * q).trailingDegree = p.trailingDegree + q.trailingDegree :=
   by
   by_cases hp : p = 0
@@ -152,6 +178,12 @@ theorem trailingDegree_mul : (p * q).trailingDegree = p.trailingDegree + q.trail
     WithTop.coe_add]
 #align polynomial.trailing_degree_mul Polynomial.trailingDegree_mul
 
+/- warning: polynomial.nat_degree_pow -> Polynomial.natDegree_pow is a dubious translation:
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+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] (p : Polynomial.{u1} R _inst_1) (n : Nat), Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) p n)) (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat Nat.hasMul) n (Polynomial.natDegree.{u1} R _inst_1 p))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_pow Polynomial.natDegree_powₓ'. -/
 @[simp]
 theorem natDegree_pow (p : R[X]) (n : ℕ) : natDegree (p ^ n) = n * natDegree p :=
   if hp0 : p = 0 then
@@ -162,6 +194,12 @@ theorem natDegree_pow (p : R[X]) (n : ℕ) : natDegree (p ^ n) = n * natDegree p
       (by rw [← leading_coeff_pow, Ne.def, leading_coeff_eq_zero] <;> exact pow_ne_zero _ hp0)
 #align polynomial.nat_degree_pow Polynomial.natDegree_pow
 
+/- warning: polynomial.degree_le_mul_left -> Polynomial.degree_le_mul_left is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.degree_le_mul_left Polynomial.degree_le_mul_leftₓ'. -/
 theorem degree_le_mul_left (p : R[X]) (hq : q ≠ 0) : degree p ≤ degree (p * q) :=
   if hp : p = 0 then by simp only [hp, MulZeroClass.zero_mul, le_refl]
   else by
@@ -169,42 +207,84 @@ theorem degree_le_mul_left (p : R[X]) (hq : q ≠ 0) : degree p ≤ degree (p *
       exact WithBot.coe_le_coe.2 (Nat.le_add_right _ _)
 #align polynomial.degree_le_mul_left Polynomial.degree_le_mul_left
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_le_of_dvd Polynomial.natDegree_le_of_dvdₓ'. -/
 theorem natDegree_le_of_dvd {p q : R[X]} (h1 : p ∣ q) (h2 : q ≠ 0) : p.natDegree ≤ q.natDegree :=
   by
   rcases h1 with ⟨q, rfl⟩; rw [mul_ne_zero_iff] at h2
   rw [nat_degree_mul h2.1 h2.2]; exact Nat.le_add_right _ _
 #align polynomial.nat_degree_le_of_dvd Polynomial.natDegree_le_of_dvd
 
+/- warning: polynomial.degree_le_of_dvd -> Polynomial.degree_le_of_dvd is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.degree_le_of_dvd Polynomial.degree_le_of_dvdₓ'. -/
 theorem degree_le_of_dvd {p q : R[X]} (h1 : p ∣ q) (h2 : q ≠ 0) : degree p ≤ degree q :=
   by
   rcases h1 with ⟨q, rfl⟩; rw [mul_ne_zero_iff] at h2
   exact degree_le_mul_left p h2.2
 #align polynomial.degree_le_of_dvd Polynomial.degree_le_of_dvd
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.eq_zero_of_dvd_of_degree_lt Polynomial.eq_zero_of_dvd_of_degree_ltₓ'. -/
 theorem eq_zero_of_dvd_of_degree_lt {p q : R[X]} (h₁ : p ∣ q) (h₂ : degree q < degree p) : q = 0 :=
   by
   by_contra hc
   exact (lt_iff_not_ge _ _).mp h₂ (degree_le_of_dvd h₁ hc)
 #align polynomial.eq_zero_of_dvd_of_degree_lt Polynomial.eq_zero_of_dvd_of_degree_lt
 
+/- warning: polynomial.eq_zero_of_dvd_of_nat_degree_lt -> Polynomial.eq_zero_of_dvd_of_natDegree_lt is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align polynomial.eq_zero_of_dvd_of_nat_degree_lt Polynomial.eq_zero_of_dvd_of_natDegree_ltₓ'. -/
 theorem eq_zero_of_dvd_of_natDegree_lt {p q : R[X]} (h₁ : p ∣ q) (h₂ : natDegree q < natDegree p) :
     q = 0 := by
   by_contra hc
   exact (lt_iff_not_ge _ _).mp h₂ (nat_degree_le_of_dvd h₁ hc)
 #align polynomial.eq_zero_of_dvd_of_nat_degree_lt Polynomial.eq_zero_of_dvd_of_natDegree_lt
 
+/- warning: polynomial.not_dvd_of_degree_lt -> Polynomial.not_dvd_of_degree_lt is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.not_dvd_of_degree_lt Polynomial.not_dvd_of_degree_ltₓ'. -/
 theorem not_dvd_of_degree_lt {p q : R[X]} (h0 : q ≠ 0) (hl : q.degree < p.degree) : ¬p ∣ q :=
   by
   by_contra hcontra
   exact h0 (eq_zero_of_dvd_of_degree_lt hcontra hl)
 #align polynomial.not_dvd_of_degree_lt Polynomial.not_dvd_of_degree_lt
 
+/- warning: polynomial.not_dvd_of_nat_degree_lt -> Polynomial.not_dvd_of_natDegree_lt is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {p : Polynomial.{u1} R _inst_1} {q : Polynomial.{u1} R _inst_1}, (Ne.{succ u1} (Polynomial.{u1} R _inst_1) q (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))) -> (LT.lt.{0} Nat Nat.hasLt (Polynomial.natDegree.{u1} R _inst_1 q) (Polynomial.natDegree.{u1} R _inst_1 p)) -> (Not (Dvd.Dvd.{u1} (Polynomial.{u1} R _inst_1) (semigroupDvd.{u1} (Polynomial.{u1} R _inst_1) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R _inst_1) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) p q))
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+Case conversion may be inaccurate. Consider using '#align polynomial.not_dvd_of_nat_degree_lt Polynomial.not_dvd_of_natDegree_ltₓ'. -/
 theorem not_dvd_of_natDegree_lt {p q : R[X]} (h0 : q ≠ 0) (hl : q.natDegree < p.natDegree) :
     ¬p ∣ q := by
   by_contra hcontra
   exact h0 (eq_zero_of_dvd_of_nat_degree_lt hcontra hl)
 #align polynomial.not_dvd_of_nat_degree_lt Polynomial.not_dvd_of_natDegree_lt
 
+/- warning: polynomial.nat_degree_sub_eq_of_prod_eq -> Polynomial.natDegree_sub_eq_of_prod_eq is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_sub_eq_of_prod_eq Polynomial.natDegree_sub_eq_of_prod_eqₓ'. -/
 /-- This lemma is useful for working with the `int_degree` of a rational function. -/
 theorem natDegree_sub_eq_of_prod_eq {p₁ p₂ q₁ q₂ : R[X]} (hp₁ : p₁ ≠ 0) (hq₁ : q₁ ≠ 0)
     (hp₂ : p₂ ≠ 0) (hq₂ : q₂ ≠ 0) (h_eq : p₁ * q₂ = p₂ * q₁) :
@@ -215,6 +295,12 @@ theorem natDegree_sub_eq_of_prod_eq {p₁ p₂ q₁ q₂ : R[X]} (hp₁ : p₁ 
   rw [← nat_degree_mul hp₁ hq₂, ← nat_degree_mul hp₂ hq₁, h_eq]
 #align polynomial.nat_degree_sub_eq_of_prod_eq Polynomial.natDegree_sub_eq_of_prod_eq
 
+/- warning: polynomial.nat_degree_eq_zero_of_is_unit -> Polynomial.natDegree_eq_zero_of_isUnit is a dubious translation:
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+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {p : Polynomial.{u1} R _inst_1}, (IsUnit.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) p) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 p) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R _inst_1}, (IsUnit.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) p) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 p) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))
+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_eq_zero_of_is_unit Polynomial.natDegree_eq_zero_of_isUnitₓ'. -/
 theorem natDegree_eq_zero_of_isUnit (h : IsUnit p) : natDegree p = 0 :=
   by
   nontriviality R
@@ -224,16 +310,34 @@ theorem natDegree_eq_zero_of_isUnit (h : IsUnit p) : natDegree p = 0 :=
   exact this.1
 #align polynomial.nat_degree_eq_zero_of_is_unit Polynomial.natDegree_eq_zero_of_isUnit
 
+/- warning: polynomial.degree_eq_zero_of_is_unit -> Polynomial.degree_eq_zero_of_isUnit is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {p : Polynomial.{u1} R _inst_1} [_inst_3 : Nontrivial.{u1} R], (IsUnit.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) p) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 p) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R _inst_1} [_inst_3 : Nontrivial.{u1} R], (IsUnit.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) p) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 p) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))))
+Case conversion may be inaccurate. Consider using '#align polynomial.degree_eq_zero_of_is_unit Polynomial.degree_eq_zero_of_isUnitₓ'. -/
 theorem degree_eq_zero_of_isUnit [Nontrivial R] (h : IsUnit p) : degree p = 0 :=
   (natDegree_eq_zero_iff_degree_le_zero.mp <| natDegree_eq_zero_of_isUnit h).antisymm
     (zero_le_degree_iff.mpr h.NeZero)
 #align polynomial.degree_eq_zero_of_is_unit Polynomial.degree_eq_zero_of_isUnit
 
+/- warning: polynomial.degree_coe_units -> Polynomial.degree_coe_units is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] [_inst_3 : Nontrivial.{u1} R] (u : Units.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))), Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{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 _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.{u1} R _inst_1) (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.{u1} R _inst_1) (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.{u1} R _inst_1) (coeBase.{succ u1, succ u1} (Units.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.{u1} R _inst_1) (Units.hasCoe.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) u)) (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 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))] [_inst_3 : Nontrivial.{u1} R] (u : Units.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))), Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 (Units.val.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) u)) (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.degree_coe_units Polynomial.degree_coe_unitsₓ'. -/
 @[simp]
 theorem degree_coe_units [Nontrivial R] (u : R[X]ˣ) : degree (u : R[X]) = 0 :=
   degree_eq_zero_of_isUnit ⟨u, rfl⟩
 #align polynomial.degree_coe_units Polynomial.degree_coe_units
 
+/- warning: polynomial.is_unit_iff -> Polynomial.isUnit_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] {p : Polynomial.{u1} R _inst_1}, Iff (IsUnit.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) p) (Exists.{succ u1} R (fun (r : R) => And (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) r) (Eq.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) r) p)))
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+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R _inst_1}, Iff (IsUnit.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) p) (Exists.{succ u1} R (fun (r : R) => And (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) r) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r) p)))
+Case conversion may be inaccurate. Consider using '#align polynomial.is_unit_iff Polynomial.isUnit_iffₓ'. -/
 theorem isUnit_iff : IsUnit p ↔ ∃ r : R, IsUnit r ∧ C r = p :=
   ⟨fun hp =>
     ⟨p.coeff 0,
@@ -282,6 +386,12 @@ section NoZeroDivisors
 
 variable [CommSemiring R] [NoZeroDivisors R] {p q : R[X]}
 
+/- warning: polynomial.irreducible_of_monic -> Polynomial.irreducible_of_monic is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) -> (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 1 (One.one.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.hasOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) -> (Iff (Irreducible.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p) (forall (f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (g : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) f) -> (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) g) -> (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) f g) p) -> (Or (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) f (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 1 (One.one.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.hasOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) g (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 1 (One.one.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.hasOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))))
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+Case conversion may be inaccurate. Consider using '#align polynomial.irreducible_of_monic Polynomial.irreducible_of_monicₓ'. -/
 theorem irreducible_of_monic (hp : p.Monic) (hp1 : p ≠ 1) :
     Irreducible p ↔ ∀ f g : R[X], f.Monic → g.Monic → f * g = p → f = 1 ∨ g = 1 :=
   by
@@ -297,6 +407,12 @@ theorem irreducible_of_monic (hp : p.Monic) (hp1 : p ≠ 1) :
       mul_comm, ← hfg]
 #align polynomial.irreducible_of_monic Polynomial.irreducible_of_monic
 
+/- warning: polynomial.monic.irreducible_iff_nat_degree -> Polynomial.Monic.irreducible_iff_natDegree is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) -> (Iff (Irreducible.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p) (And (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 1 (One.one.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.hasOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (forall (f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (g : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) f) -> (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) g) -> (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) f g) p) -> (Or (Eq.{1} Nat (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) f) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (Eq.{1} Nat (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) g) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) -> (Iff (Irreducible.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p) (And (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (forall (f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (g : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) f) -> (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) g) -> (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) f g) p) -> (Or (Eq.{1} Nat (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) f) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (Eq.{1} Nat (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) g) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.monic.irreducible_iff_nat_degree Polynomial.Monic.irreducible_iff_natDegreeₓ'. -/
 theorem Monic.irreducible_iff_natDegree (hp : p.Monic) :
     Irreducible p ↔
       p ≠ 1 ∧ ∀ f g : R[X], f.Monic → g.Monic → f * g = p → f.natDegree = 0 ∨ g.natDegree = 0 :=
@@ -307,7 +423,13 @@ theorem Monic.irreducible_iff_natDegree (hp : p.Monic) :
   rw [ha.nat_degree_eq_zero_iff_eq_one, hb.nat_degree_eq_zero_iff_eq_one]
 #align polynomial.monic.irreducible_iff_nat_degree Polynomial.Monic.irreducible_iff_natDegree
 
-theorem Monic.irreducible_iff_nat_degree' (hp : p.Monic) :
+/- warning: polynomial.monic.irreducible_iff_nat_degree' -> Polynomial.Monic.irreducible_iff_natDegree' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) -> (Iff (Irreducible.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p) (And (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 1 (One.one.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.hasOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (forall (f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (g : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) f) -> (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) g) -> (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) f g) p) -> (Not (Membership.Mem.{0, 0} Nat (Finset.{0} Nat) (Finset.hasMem.{0} Nat) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) g) (Finset.Ioc.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (HDiv.hDiv.{0, 0, 0} Nat Nat Nat (instHDiv.{0} Nat Nat.hasDiv) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) -> (Iff (Irreducible.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p) (And (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (forall (f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (g : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) f) -> (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) g) -> (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) f g) p) -> (Not (Membership.mem.{0, 0} Nat (Finset.{0} Nat) (Finset.instMembershipFinset.{0} Nat) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) g) (Finset.Ioc.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) instLocallyFiniteOrderNatToPreorderToPartialOrderStrictOrderedSemiring (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (HDiv.hDiv.{0, 0, 0} Nat Nat Nat (instHDiv.{0} Nat Nat.instDivNat) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.monic.irreducible_iff_nat_degree' Polynomial.Monic.irreducible_iff_natDegree'ₓ'. -/
+theorem Monic.irreducible_iff_natDegree' (hp : p.Monic) :
     Irreducible p ↔
       p ≠ 1 ∧ ∀ f g : R[X], f.Monic → g.Monic → f * g = p → g.natDegree ∉ Ioc 0 (p.natDegree / 2) :=
   by
@@ -321,8 +443,14 @@ theorem Monic.irreducible_iff_nat_degree' (hp : p.Monic) :
     obtain hl | hl := le_total f.nat_degree g.nat_degree
     · exact ⟨g, f, hg, hf, mul_comm g f, h.1, add_le_add_left hl _⟩
     · exact ⟨f, g, hf, hg, rfl, h.2, add_le_add_right hl _⟩
-#align polynomial.monic.irreducible_iff_nat_degree' Polynomial.Monic.irreducible_iff_nat_degree'
-
+#align polynomial.monic.irreducible_iff_nat_degree' Polynomial.Monic.irreducible_iff_natDegree'
+
+/- warning: polynomial.monic.not_irreducible_iff_exists_add_mul_eq_coeff -> Polynomial.Monic.not_irreducible_iff_exists_add_mul_eq_coeff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> (Iff (Not (Irreducible.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p)) (Exists.{succ u1} R (fun (c₁ : R) => Exists.{succ u1} R (fun (c₂ : R) => And (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) c₁ c₂)) (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) c₁ c₂))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) -> (Iff (Not (Irreducible.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p)) (Exists.{succ u1} R (fun (c₁ : R) => Exists.{succ u1} R (fun (c₂ : R) => And (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) c₁ c₂)) (Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) c₁ c₂))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.monic.not_irreducible_iff_exists_add_mul_eq_coeff Polynomial.Monic.not_irreducible_iff_exists_add_mul_eq_coeffₓ'. -/
 theorem Monic.not_irreducible_iff_exists_add_mul_eq_coeff (hm : p.Monic) (hnd : p.natDegree = 2) :
     ¬Irreducible p ↔ ∃ c₁ c₂, p.coeff 0 = c₁ * c₂ ∧ p.coeff 1 = c₁ + c₂ :=
   by
@@ -345,10 +473,22 @@ theorem Monic.not_irreducible_iff_exists_add_mul_eq_coeff (hm : p.Monic) (hnd :
     simpa only [nat_degree_one] using hnd
 #align polynomial.monic.not_irreducible_iff_exists_add_mul_eq_coeff Polynomial.Monic.not_irreducible_iff_exists_add_mul_eq_coeff
 
+/- warning: polynomial.root_mul -> Polynomial.root_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {a : R} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, Iff (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) p q) a) (Or (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p a) (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) q a))
+but is expected to have type
+  forall {R : Type.{u1}} {a : R} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, Iff (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) p q) a) (Or (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p a) (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) q a))
+Case conversion may be inaccurate. Consider using '#align polynomial.root_mul Polynomial.root_mulₓ'. -/
 theorem root_mul : IsRoot (p * q) a ↔ IsRoot p a ∨ IsRoot q a := by
   simp_rw [is_root, eval_mul, mul_eq_zero]
 #align polynomial.root_mul Polynomial.root_mul
 
+/- warning: polynomial.root_or_root_of_root_mul -> Polynomial.root_or_root_of_root_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {a : R} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) p q) a) -> (Or (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p a) (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) q a))
+but is expected to have type
+  forall {R : Type.{u1}} {a : R} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))] {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) p q) a) -> (Or (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p a) (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) q a))
+Case conversion may be inaccurate. Consider using '#align polynomial.root_or_root_of_root_mul Polynomial.root_or_root_of_root_mulₓ'. -/
 theorem root_or_root_of_root_mul (h : IsRoot (p * q) a) : IsRoot p a ∨ IsRoot q a :=
   root_mul.1 h
 #align polynomial.root_or_root_of_root_mul Polynomial.root_or_root_of_root_mul
@@ -368,6 +508,12 @@ section CommRing
 
 variable [CommRing R]
 
+/- warning: polynomial.le_root_multiplicity_iff -> Polynomial.le_rootMultiplicity_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (forall {a : R} {n : Nat}, Iff (LE.le.{0} Nat Nat.hasLe n (Polynomial.rootMultiplicity.{u1} R _inst_1 a p)) (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) n) p))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) -> (forall {a : R} {n : Nat}, Iff (LE.le.{0} Nat instLENat n (Polynomial.rootMultiplicity.{u1} R _inst_1 a p)) (Dvd.dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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 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(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))) a)) n) p))
+Case conversion may be inaccurate. Consider using '#align polynomial.le_root_multiplicity_iff Polynomial.le_rootMultiplicity_iffₓ'. -/
 /-- The multiplicity of `a` as root of a nonzero polynomial `p` is at least `n` iff
   `(X - a) ^ n` divides `p`. -/
 theorem le_rootMultiplicity_iff {p : R[X]} (p0 : p ≠ 0) {a : R} {n : ℕ} :
@@ -380,15 +526,33 @@ theorem le_rootMultiplicity_iff {p : R[X]} (p0 : p ≠ 0) {a : R} {n : ℕ} :
     apply one_dvd; · exact h n n.lt_succ_self
 #align polynomial.le_root_multiplicity_iff Polynomial.le_rootMultiplicity_iff
 
+/- warning: polynomial.root_multiplicity_le_iff -> Polynomial.rootMultiplicity_le_iff is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) -> (forall (a : R) (n : Nat), Iff (LE.le.{0} Nat instLENat (Polynomial.rootMultiplicity.{u1} R _inst_1 a p) n) (Not (Dvd.dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R 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(Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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 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+Case conversion may be inaccurate. Consider using '#align polynomial.root_multiplicity_le_iff Polynomial.rootMultiplicity_le_iffₓ'. -/
 theorem rootMultiplicity_le_iff {p : R[X]} (p0 : p ≠ 0) (a : R) (n : ℕ) :
     rootMultiplicity a p ≤ n ↔ ¬(X - C a) ^ (n + 1) ∣ p := by
   rw [← (le_root_multiplicity_iff p0).Not, not_le, Nat.lt_add_one_iff]
 #align polynomial.root_multiplicity_le_iff Polynomial.rootMultiplicity_le_iff
 
+/- warning: polynomial.pow_root_multiplicity_not_dvd -> Polynomial.pow_rootMultiplicity_not_dvd is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align polynomial.pow_root_multiplicity_not_dvd Polynomial.pow_rootMultiplicity_not_dvdₓ'. -/
 theorem pow_rootMultiplicity_not_dvd {p : R[X]} (p0 : p ≠ 0) (a : R) :
     ¬(X - C a) ^ (rootMultiplicity a p + 1) ∣ p := by rw [← root_multiplicity_le_iff p0]
 #align polynomial.pow_root_multiplicity_not_dvd Polynomial.pow_rootMultiplicity_not_dvd
 
+/- warning: polynomial.root_multiplicity_add -> Polynomial.rootMultiplicity_add is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align polynomial.root_multiplicity_add Polynomial.rootMultiplicity_addₓ'. -/
 /-- The multiplicity of `p + q` is at least the minimum of the multiplicities. -/
 theorem rootMultiplicity_add {p q : R[X]} (a : R) (hzero : p + q ≠ 0) :
     min (rootMultiplicity a p) (rootMultiplicity a q) ≤ rootMultiplicity a (p + q) :=
@@ -405,36 +569,70 @@ section Roots
 
 open Multiset
 
-theorem prime_x_sub_c (r : R) : Prime (X - C r) :=
+/- warning: polynomial.prime_X_sub_C -> Polynomial.prime_X_sub_C is a dubious translation:
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(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))) r))
+Case conversion may be inaccurate. Consider using '#align polynomial.prime_X_sub_C Polynomial.prime_X_sub_Cₓ'. -/
+theorem prime_X_sub_C (r : R) : Prime (X - C r) :=
   ⟨X_sub_C_ne_zero r, not_isUnit_X_sub_C r, fun _ _ =>
     by
     simp_rw [dvd_iff_is_root, is_root.def, eval_mul, mul_eq_zero]
     exact id⟩
-#align polynomial.prime_X_sub_C Polynomial.prime_x_sub_c
+#align polynomial.prime_X_sub_C Polynomial.prime_X_sub_C
 
-theorem prime_x : Prime (X : R[X]) :=
+#print Polynomial.prime_X /-
+theorem prime_X : Prime (X : R[X]) :=
   by
   convert prime_X_sub_C (0 : R)
   simp
-#align polynomial.prime_X Polynomial.prime_x
+#align polynomial.prime_X Polynomial.prime_X
+-/
 
+#print Polynomial.Monic.prime_of_degree_eq_one /-
 theorem Monic.prime_of_degree_eq_one (hp1 : degree p = 1) (hm : Monic p) : Prime p :=
   have : p = X - C (-p.coeff 0) := by simpa [hm.leading_coeff] using eq_X_add_C_of_degree_eq_one hp1
-  this.symm ▸ prime_x_sub_c _
+  this.symm ▸ prime_X_sub_C _
 #align polynomial.monic.prime_of_degree_eq_one Polynomial.Monic.prime_of_degree_eq_one
+-/
 
-theorem irreducible_x_sub_c (r : R) : Irreducible (X - C r) :=
-  (prime_x_sub_c r).Irreducible
-#align polynomial.irreducible_X_sub_C Polynomial.irreducible_x_sub_c
-
-theorem irreducible_x : Irreducible (X : R[X]) :=
-  Prime.irreducible prime_x
-#align polynomial.irreducible_X Polynomial.irreducible_x
-
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+Case conversion may be inaccurate. Consider using '#align polynomial.irreducible_X_sub_C Polynomial.irreducible_X_sub_Cₓ'. -/
+theorem irreducible_X_sub_C (r : R) : Irreducible (X - C r) :=
+  (prime_X_sub_C r).Irreducible
+#align polynomial.irreducible_X_sub_C Polynomial.irreducible_X_sub_C
+
+/- warning: polynomial.irreducible_X -> Polynomial.irreducible_X 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.irreducible_X Polynomial.irreducible_Xₓ'. -/
+theorem irreducible_X : Irreducible (X : R[X]) :=
+  Prime.irreducible prime_X
+#align polynomial.irreducible_X Polynomial.irreducible_X
+
+/- warning: polynomial.monic.irreducible_of_degree_eq_one -> Polynomial.Monic.irreducible_of_degree_eq_one is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.monic.irreducible_of_degree_eq_one Polynomial.Monic.irreducible_of_degree_eq_oneₓ'. -/
 theorem Monic.irreducible_of_degree_eq_one (hp1 : degree p = 1) (hm : Monic p) : Irreducible p :=
   (hm.prime_of_degree_eq_one hp1).Irreducible
 #align polynomial.monic.irreducible_of_degree_eq_one Polynomial.Monic.irreducible_of_degree_eq_one
 
+/- warning: polynomial.eq_of_monic_of_associated -> Polynomial.eq_of_monic_of_associated is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.eq_of_monic_of_associated Polynomial.eq_of_monic_of_associatedₓ'. -/
 theorem eq_of_monic_of_associated (hp : p.Monic) (hq : q.Monic) (hpq : Associated p q) : p = q :=
   by
   obtain ⟨u, hu⟩ := hpq
@@ -445,6 +643,7 @@ theorem eq_of_monic_of_associated (hp : p.Monic) (hq : q.Monic) (hpq : Associate
   all_goals infer_instance
 #align polynomial.eq_of_monic_of_associated Polynomial.eq_of_monic_of_associated
 
+#print Polynomial.rootMultiplicity_mul /-
 theorem rootMultiplicity_mul {p q : R[X]} {x : R} (hpq : p * q ≠ 0) :
     rootMultiplicity x (p * q) = rootMultiplicity x p + rootMultiplicity x q :=
   by
@@ -454,23 +653,42 @@ theorem rootMultiplicity_mul {p q : R[X]} {x : R} (hpq : p * q ≠ 0) :
     dif_neg hp, root_multiplicity_eq_multiplicity q, dif_neg hq,
     multiplicity.mul' (prime_X_sub_C x)]
 #align polynomial.root_multiplicity_mul Polynomial.rootMultiplicity_mul
+-/
 
-theorem rootMultiplicity_x_sub_c_self {x : R} : rootMultiplicity x (X - C x) = 1 := by
+/- warning: polynomial.root_multiplicity_X_sub_C_self -> Polynomial.rootMultiplicity_X_sub_C_self is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.root_multiplicity_X_sub_C_self Polynomial.rootMultiplicity_X_sub_C_selfₓ'. -/
+theorem rootMultiplicity_X_sub_C_self {x : R} : rootMultiplicity x (X - C x) = 1 := by
   rw [root_multiplicity_eq_multiplicity, dif_neg (X_sub_C_ne_zero x),
     multiplicity.get_multiplicity_self]
-#align polynomial.root_multiplicity_X_sub_C_self Polynomial.rootMultiplicity_x_sub_c_self
-
-theorem rootMultiplicity_x_sub_c {x y : R} :
+#align polynomial.root_multiplicity_X_sub_C_self Polynomial.rootMultiplicity_X_sub_C_self
+
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+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))] {x : R} {y : R}, Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 x (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) y) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) y))) (ite.{1} Nat (Eq.{succ u1} R x y) (Classical.propDecidable (Eq.{succ u1} R x y)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))
+Case conversion may be inaccurate. Consider using '#align polynomial.root_multiplicity_X_sub_C Polynomial.rootMultiplicity_X_sub_Cₓ'. -/
+theorem rootMultiplicity_X_sub_C {x y : R} :
     rootMultiplicity x (X - C y) = if x = y then 1 else 0 :=
   by
   split_ifs with hxy
   · rw [hxy]
     exact root_multiplicity_X_sub_C_self
   exact root_multiplicity_eq_zero (mt root_X_sub_C.mp (Ne.symm hxy))
-#align polynomial.root_multiplicity_X_sub_C Polynomial.rootMultiplicity_x_sub_c
-
+#align polynomial.root_multiplicity_X_sub_C Polynomial.rootMultiplicity_X_sub_C
+
+/- warning: polynomial.root_multiplicity_X_sub_C_pow -> Polynomial.rootMultiplicity_X_sub_C_pow is a dubious translation:
+lean 3 declaration is
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+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))] (a : R) (n : Nat), Eq.{1} Nat (Polynomial.rootMultiplicity.{u1} R _inst_1 a (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{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))) (Semiring.toMonoidWithZero.{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))))))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R 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(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))) a)) n)) n
+Case conversion may be inaccurate. Consider using '#align polynomial.root_multiplicity_X_sub_C_pow Polynomial.rootMultiplicity_X_sub_C_powₓ'. -/
 /-- The multiplicity of `a` as root of `(X - a) ^ n` is `n`. -/
-theorem rootMultiplicity_x_sub_c_pow (a : R) (n : ℕ) : rootMultiplicity a ((X - C a) ^ n) = n :=
+theorem rootMultiplicity_X_sub_C_pow (a : R) (n : ℕ) : rootMultiplicity a ((X - C a) ^ n) = n :=
   by
   induction' n with n hn
   · refine' root_multiplicity_eq_zero _
@@ -478,8 +696,14 @@ theorem rootMultiplicity_x_sub_c_pow (a : R) (n : ℕ) : rootMultiplicity a ((X
   have hzero := pow_ne_zero n.succ (X_sub_C_ne_zero a)
   rw [pow_succ (X - C a) n] at hzero⊢
   simp only [root_multiplicity_mul hzero, root_multiplicity_X_sub_C_self, hn, Nat.one_add]
-#align polynomial.root_multiplicity_X_sub_C_pow Polynomial.rootMultiplicity_x_sub_c_pow
-
+#align polynomial.root_multiplicity_X_sub_C_pow Polynomial.rootMultiplicity_X_sub_C_pow
+
+/- warning: polynomial.exists_multiset_roots -> Polynomial.exists_multiset_roots is a dubious translation:
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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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (Exists.{succ u1} (Multiset.{u1} R) (fun (s : Multiset.{u1} R) => And (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) s)) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) (forall (a : R), Eq.{1} Nat (Multiset.count.{u1} R (fun (a : R) (b : R) => Classical.propDecidable (Eq.{succ u1} R a b)) a s) (Polynomial.rootMultiplicity.{u1} R _inst_1 a p))))
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+Case conversion may be inaccurate. Consider using '#align polynomial.exists_multiset_roots Polynomial.exists_multiset_rootsₓ'. -/
 theorem exists_multiset_roots :
     ∀ {p : R[X]} (hp : p ≠ 0),
       ∃ s : Multiset R, (s.card : WithBot ℕ) ≤ degree p ∧ ∀ a, s.count a = rootMultiplicity a p
@@ -522,17 +746,27 @@ theorem exists_multiset_roots :
         rw [count_zero, root_multiplicity_eq_zero (not_exists.mp h a)]⟩
 #align polynomial.exists_multiset_roots Polynomial.exists_multiset_roots
 
+#print Polynomial.roots /-
 /-- `roots p` noncomputably gives a multiset containing all the roots of `p`,
 including their multiplicities. -/
 noncomputable def roots (p : R[X]) : Multiset R :=
   if h : p = 0 then ∅ else Classical.choose (exists_multiset_roots h)
 #align polynomial.roots Polynomial.roots
+-/
 
+#print Polynomial.roots_zero /-
 @[simp]
 theorem roots_zero : (0 : R[X]).roots = 0 :=
   dif_pos rfl
 #align polynomial.roots_zero Polynomial.roots_zero
+-/
 
+/- warning: polynomial.card_roots -> Polynomial.card_roots is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.card_roots Polynomial.card_rootsₓ'. -/
 theorem card_roots (hp0 : p ≠ 0) : ((roots p).card : WithBot ℕ) ≤ degree p :=
   by
   unfold roots
@@ -540,6 +774,12 @@ theorem card_roots (hp0 : p ≠ 0) : ((roots p).card : WithBot ℕ) ≤ degree p
   exact (Classical.choose_spec (exists_multiset_roots hp0)).1
 #align polynomial.card_roots Polynomial.card_roots
 
+/- warning: polynomial.card_roots' -> Polynomial.card_roots' is a dubious translation:
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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))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), LE.le.{0} Nat Nat.hasLe (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{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))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) instLENat (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)
+Case conversion may be inaccurate. Consider using '#align polynomial.card_roots' Polynomial.card_roots'ₓ'. -/
 theorem card_roots' (p : R[X]) : p.roots.card ≤ natDegree p :=
   by
   by_cases hp0 : p = 0
@@ -547,22 +787,35 @@ theorem card_roots' (p : R[X]) : p.roots.card ≤ natDegree p :=
   exact WithBot.coe_le_coe.1 (le_trans (card_roots hp0) (le_of_eq <| degree_eq_nat_degree hp0))
 #align polynomial.card_roots' Polynomial.card_roots'
 
-theorem card_roots_sub_c {p : R[X]} {a : R} (hp0 : 0 < degree p) :
+/- warning: polynomial.card_roots_sub_C -> Polynomial.card_roots_sub_C is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align polynomial.card_roots_sub_C Polynomial.card_roots_sub_Cₓ'. -/
+theorem card_roots_sub_C {p : R[X]} {a : R} (hp0 : 0 < degree p) :
     ((p - C a).roots.card : WithBot ℕ) ≤ degree p :=
   calc
     ((p - C a).roots.card : WithBot ℕ) ≤ degree (p - C a) :=
       card_roots <| mt sub_eq_zero.1 fun h => not_le_of_gt hp0 <| h.symm ▸ degree_C_le
     _ = degree p := by rw [sub_eq_add_neg, ← C_neg] <;> exact degree_add_C hp0
     
-#align polynomial.card_roots_sub_C Polynomial.card_roots_sub_c
-
+#align polynomial.card_roots_sub_C Polynomial.card_roots_sub_C
+
+/- warning: polynomial.card_roots_sub_C' -> Polynomial.card_roots_sub_C' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.card_roots_sub_C' Polynomial.card_roots_sub_C'ₓ'. -/
 theorem card_roots_sub_C' {p : R[X]} {a : R} (hp0 : 0 < degree p) :
     (p - C a).roots.card ≤ natDegree p :=
   WithBot.coe_le_coe.1
-    (le_trans (card_roots_sub_c hp0)
+    (le_trans (card_roots_sub_C hp0)
       (le_of_eq <| degree_eq_natDegree fun h => by simp_all [lt_irrefl]))
 #align polynomial.card_roots_sub_C' Polynomial.card_roots_sub_C'
 
+#print Polynomial.count_roots /-
 @[simp]
 theorem count_roots (p : R[X]) : p.roots.count a = rootMultiplicity a p :=
   by
@@ -571,108 +824,182 @@ theorem count_roots (p : R[X]) : p.roots.count a = rootMultiplicity a p :=
   rw [roots, dif_neg hp]
   exact (Classical.choose_spec (exists_multiset_roots hp)).2 a
 #align polynomial.count_roots Polynomial.count_roots
+-/
 
+#print Polynomial.mem_roots' /-
 @[simp]
 theorem mem_roots' : a ∈ p.roots ↔ p ≠ 0 ∧ IsRoot p a := by
   rw [← count_pos, count_roots p, root_multiplicity_pos']
 #align polynomial.mem_roots' Polynomial.mem_roots'
+-/
 
+#print Polynomial.mem_roots /-
 theorem mem_roots (hp : p ≠ 0) : a ∈ p.roots ↔ IsRoot p a :=
   mem_roots'.trans <| and_iff_right hp
 #align polynomial.mem_roots Polynomial.mem_roots
+-/
 
+#print Polynomial.ne_zero_of_mem_roots /-
 theorem ne_zero_of_mem_roots (h : a ∈ p.roots) : p ≠ 0 :=
   (mem_roots'.1 h).1
 #align polynomial.ne_zero_of_mem_roots Polynomial.ne_zero_of_mem_roots
+-/
 
+#print Polynomial.isRoot_of_mem_roots /-
 theorem isRoot_of_mem_roots (h : a ∈ p.roots) : IsRoot p a :=
   (mem_roots'.1 h).2
 #align polynomial.is_root_of_mem_roots Polynomial.isRoot_of_mem_roots
+-/
 
+#print Polynomial.card_le_degree_of_subset_roots /-
 theorem card_le_degree_of_subset_roots {p : R[X]} {Z : Finset R} (h : Z.val ⊆ p.roots) :
     Z.card ≤ p.natDegree :=
   (Multiset.card_le_of_le (Finset.val_le_iff_val_subset.2 h)).trans (Polynomial.card_roots' p)
 #align polynomial.card_le_degree_of_subset_roots Polynomial.card_le_degree_of_subset_roots
+-/
 
+#print Polynomial.finite_setOf_isRoot /-
 theorem finite_setOf_isRoot {p : R[X]} (hp : p ≠ 0) : Set.Finite { x | IsRoot p x } := by
   simpa only [← Finset.setOf_mem, mem_to_finset, mem_roots hp] using p.roots.to_finset.finite_to_set
 #align polynomial.finite_set_of_is_root Polynomial.finite_setOf_isRoot
+-/
 
+#print Polynomial.eq_zero_of_infinite_isRoot /-
 theorem eq_zero_of_infinite_isRoot (p : R[X]) (h : Set.Infinite { x | IsRoot p x }) : p = 0 :=
   not_imp_comm.mp finite_setOf_isRoot h
 #align polynomial.eq_zero_of_infinite_is_root Polynomial.eq_zero_of_infinite_isRoot
+-/
 
+#print Polynomial.exists_max_root /-
 theorem exists_max_root [LinearOrder R] (p : R[X]) (hp : p ≠ 0) : ∃ x₀, ∀ x, p.IsRoot x → x ≤ x₀ :=
   Set.exists_upper_bound_image _ _ <| finite_setOf_isRoot hp
 #align polynomial.exists_max_root Polynomial.exists_max_root
+-/
 
+#print Polynomial.exists_min_root /-
 theorem exists_min_root [LinearOrder R] (p : R[X]) (hp : p ≠ 0) : ∃ x₀, ∀ x, p.IsRoot x → x₀ ≤ x :=
   Set.exists_lower_bound_image _ _ <| finite_setOf_isRoot hp
 #align polynomial.exists_min_root Polynomial.exists_min_root
+-/
 
+#print Polynomial.eq_of_infinite_eval_eq /-
 theorem eq_of_infinite_eval_eq (p q : R[X]) (h : Set.Infinite { x | eval x p = eval x q }) :
     p = q := by
   rw [← sub_eq_zero]
   apply eq_zero_of_infinite_is_root
   simpa only [is_root, eval_sub, sub_eq_zero]
 #align polynomial.eq_of_infinite_eval_eq Polynomial.eq_of_infinite_eval_eq
+-/
 
+#print Polynomial.roots_mul /-
 theorem roots_mul {p q : R[X]} (hpq : p * q ≠ 0) : (p * q).roots = p.roots + q.roots :=
   Multiset.ext.mpr fun r => by
     rw [count_add, count_roots, count_roots, count_roots, root_multiplicity_mul hpq]
 #align polynomial.roots_mul Polynomial.roots_mul
+-/
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.roots.le_of_dvd Polynomial.roots.le_of_dvdₓ'. -/
 theorem roots.le_of_dvd (h : q ≠ 0) : p ∣ q → roots p ≤ roots q :=
   by
   rintro ⟨k, rfl⟩
   exact multiset.le_iff_exists_add.mpr ⟨k.roots, roots_mul h⟩
 #align polynomial.roots.le_of_dvd Polynomial.roots.le_of_dvd
 
+/- warning: polynomial.mem_roots_sub_C' -> Polynomial.mem_roots_sub_C' is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align polynomial.mem_roots_sub_C' Polynomial.mem_roots_sub_C'ₓ'. -/
 theorem mem_roots_sub_C' {p : R[X]} {a x : R} : x ∈ (p - C a).roots ↔ p ≠ C a ∧ p.eval x = a := by
   rw [mem_roots', is_root.def, sub_ne_zero, eval_sub, sub_eq_zero, eval_C]
 #align polynomial.mem_roots_sub_C' Polynomial.mem_roots_sub_C'
 
-theorem mem_roots_sub_c {p : R[X]} {a x : R} (hp0 : 0 < degree p) :
+/- warning: polynomial.mem_roots_sub_C -> Polynomial.mem_roots_sub_C 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.mem_roots_sub_C Polynomial.mem_roots_sub_Cₓ'. -/
+theorem mem_roots_sub_C {p : R[X]} {a x : R} (hp0 : 0 < degree p) :
     x ∈ (p - C a).roots ↔ p.eval x = a :=
   mem_roots_sub_C'.trans <| and_iff_right fun hp => hp0.not_le <| hp.symm ▸ degree_C_le
-#align polynomial.mem_roots_sub_C Polynomial.mem_roots_sub_c
-
+#align polynomial.mem_roots_sub_C Polynomial.mem_roots_sub_C
+
+/- warning: polynomial.roots_X_sub_C -> Polynomial.roots_X_sub_C 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.roots_X_sub_C Polynomial.roots_X_sub_Cₓ'. -/
 @[simp]
-theorem roots_x_sub_c (r : R) : roots (X - C r) = {r} :=
+theorem roots_X_sub_C (r : R) : roots (X - C r) = {r} :=
   by
   ext s
   rw [count_roots, root_multiplicity_X_sub_C, count_singleton]
-#align polynomial.roots_X_sub_C Polynomial.roots_x_sub_c
-
+#align polynomial.roots_X_sub_C Polynomial.roots_X_sub_C
+
+/- warning: polynomial.roots_X -> Polynomial.roots_X 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))], Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Singleton.singleton.{u1, u1} R (Multiset.{u1} R) (Multiset.hasSingleton.{u1} R) (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 (CommRing.toRing.{u1} R _inst_1))))))))))
+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))], Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Singleton.singleton.{u1, u1} R (Multiset.{u1} R) (Multiset.instSingletonMultiset.{u1} R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_2))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.roots_X Polynomial.roots_Xₓ'. -/
 @[simp]
-theorem roots_x : roots (X : R[X]) = {0} := by rw [← roots_X_sub_C, C_0, sub_zero]
-#align polynomial.roots_X Polynomial.roots_x
-
+theorem roots_X : roots (X : R[X]) = {0} := by rw [← roots_X_sub_C, C_0, sub_zero]
+#align polynomial.roots_X Polynomial.roots_X
+
+/- warning: polynomial.roots_C -> Polynomial.roots_C is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.roots_C Polynomial.roots_Cₓ'. -/
 @[simp]
-theorem roots_c (x : R) : (C x).roots = 0 :=
+theorem roots_C (x : R) : (C x).roots = 0 :=
   if H : x = 0 then by rw [H, C_0, roots_zero]
   else
     Multiset.ext.mpr fun r => by
       rw [count_roots, count_zero, root_multiplicity_eq_zero (not_is_root_C _ _ H)]
-#align polynomial.roots_C Polynomial.roots_c
+#align polynomial.roots_C Polynomial.roots_C
 
+#print Polynomial.roots_one /-
 @[simp]
 theorem roots_one : (1 : R[X]).roots = ∅ :=
-  roots_c 1
+  roots_C 1
 #align polynomial.roots_one Polynomial.roots_one
+-/
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.roots_C_mul Polynomial.roots_C_mulₓ'. -/
 @[simp]
-theorem roots_c_mul (p : R[X]) (ha : a ≠ 0) : (C a * p).roots = p.roots := by
+theorem roots_C_mul (p : R[X]) (ha : a ≠ 0) : (C a * p).roots = p.roots := by
   by_cases hp : p = 0 <;>
     simp only [roots_mul, *, Ne.def, mul_eq_zero, C_eq_zero, or_self_iff, not_false_iff, roots_C,
       zero_add, MulZeroClass.mul_zero]
-#align polynomial.roots_C_mul Polynomial.roots_c_mul
-
+#align polynomial.roots_C_mul Polynomial.roots_C_mul
+
+/- warning: polynomial.roots_smul_nonzero -> Polynomial.roots_smul_nonzero is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.roots_smul_nonzero Polynomial.roots_smul_nonzeroₓ'. -/
 @[simp]
 theorem roots_smul_nonzero (p : R[X]) (ha : a ≠ 0) : (a • p).roots = p.roots := by
   rw [smul_eq_C_mul, roots_C_mul _ ha]
 #align polynomial.roots_smul_nonzero Polynomial.roots_smul_nonzero
 
+#print Polynomial.roots_list_prod /-
 theorem roots_list_prod (L : List R[X]) :
     (0 : R[X]) ∉ L → L.Prod.roots = (L : Multiset R[X]).bind roots :=
   List.recOn L (fun _ => roots_one) fun hd tl ih H =>
@@ -681,13 +1008,22 @@ theorem roots_list_prod (L : List R[X]) :
     rw [List.prod_cons, roots_mul (mul_ne_zero (Ne.symm H.1) <| List.prod_ne_zero H.2), ←
       Multiset.cons_coe, Multiset.cons_bind, ih H.2]
 #align polynomial.roots_list_prod Polynomial.roots_list_prod
+-/
 
+#print Polynomial.roots_multiset_prod /-
 theorem roots_multiset_prod (m : Multiset R[X]) : (0 : R[X]) ∉ m → m.Prod.roots = m.bind roots :=
   by
   rcases m with ⟨L⟩
   simpa only [Multiset.coe_prod, quot_mk_to_coe''] using roots_list_prod L
 #align polynomial.roots_multiset_prod Polynomial.roots_multiset_prod
+-/
 
+/- warning: polynomial.roots_prod -> Polynomial.roots_prod is a dubious translation:
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+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] [_inst_2 : IsDomain.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))] {ι : Type.{u1}} (f : ι -> (Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) (s : Finset.{u1} ι), (Ne.{succ u2} (Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Finset.prod.{u2, u1} (Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Polynomial.commRing.{u2} R _inst_1)) s f) (OfNat.ofNat.{u2} (Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Polynomial.zero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) -> (Eq.{succ u2} (Multiset.{u2} R) (Polynomial.roots.{u2} R _inst_1 _inst_2 (Finset.prod.{u2, u1} (Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Polynomial.commRing.{u2} R _inst_1)) s f)) (Multiset.bind.{u1, u2} ι R (Finset.val.{u1} ι s) (fun (i : ι) => Polynomial.roots.{u2} R _inst_1 _inst_2 (f i))))
+Case conversion may be inaccurate. Consider using '#align polynomial.roots_prod Polynomial.roots_prodₓ'. -/
 theorem roots_prod {ι : Type _} (f : ι → R[X]) (s : Finset ι) :
     s.Prod f ≠ 0 → (s.Prod f).roots = s.val.bind fun i => roots (f i) :=
   by
@@ -695,6 +1031,12 @@ theorem roots_prod {ι : Type _} (f : ι → R[X]) (s : Finset ι) :
   simpa [Multiset.prod_eq_zero_iff, bind_map] using roots_multiset_prod (m.map f)
 #align polynomial.roots_prod Polynomial.roots_prod
 
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.roots_pow Polynomial.roots_powₓ'. -/
 @[simp]
 theorem roots_pow (p : R[X]) (n : ℕ) : (p ^ n).roots = n • p.roots :=
   by
@@ -707,35 +1049,71 @@ theorem roots_pow (p : R[X]) (n : ℕ) : (p ^ n).roots = n • p.roots :=
         add_smul, one_smul]
 #align polynomial.roots_pow Polynomial.roots_pow
 
-theorem roots_x_pow (n : ℕ) : (X ^ n : R[X]).roots = n • {0} := by rw [roots_pow, roots_X]
-#align polynomial.roots_X_pow Polynomial.roots_x_pow
-
-theorem roots_c_mul_x_pow (ha : a ≠ 0) (n : ℕ) : (C a * X ^ n).roots = n • {0} := by
+/- warning: polynomial.roots_X_pow -> Polynomial.roots_X_pow is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.roots_X_pow Polynomial.roots_X_powₓ'. -/
+theorem roots_X_pow (n : ℕ) : (X ^ n : R[X]).roots = n • {0} := by rw [roots_pow, roots_X]
+#align polynomial.roots_X_pow Polynomial.roots_X_pow
+
+/- warning: polynomial.roots_C_mul_X_pow -> Polynomial.roots_C_mul_X_pow is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align polynomial.roots_C_mul_X_pow Polynomial.roots_C_mul_X_powₓ'. -/
+theorem roots_C_mul_X_pow (ha : a ≠ 0) (n : ℕ) : (C a * X ^ n).roots = n • {0} := by
   rw [roots_C_mul _ ha, roots_X_pow]
-#align polynomial.roots_C_mul_X_pow Polynomial.roots_c_mul_x_pow
-
+#align polynomial.roots_C_mul_X_pow Polynomial.roots_C_mul_X_pow
+
+/- warning: polynomial.roots_monomial -> Polynomial.roots_monomial is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.roots_monomial Polynomial.roots_monomialₓ'. -/
 @[simp]
 theorem roots_monomial (ha : a ≠ 0) (n : ℕ) : (monomial n a).roots = n • {0} := by
   rw [← C_mul_X_pow_eq_monomial, roots_C_mul_X_pow ha]
 #align polynomial.roots_monomial Polynomial.roots_monomial
 
-theorem roots_prod_x_sub_c (s : Finset R) : (s.Prod fun a => X - C a).roots = s.val :=
+/- warning: polynomial.roots_prod_X_sub_C -> Polynomial.roots_prod_X_sub_C is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.roots_prod_X_sub_C Polynomial.roots_prod_X_sub_Cₓ'. -/
+theorem roots_prod_X_sub_C (s : Finset R) : (s.Prod fun a => X - C a).roots = s.val :=
   (roots_prod (fun a => X - C a) s (prod_ne_zero_iff.mpr fun a _ => X_sub_C_ne_zero a)).trans
     (by simp_rw [roots_X_sub_C, Multiset.bind_singleton, Multiset.map_id'])
-#align polynomial.roots_prod_X_sub_C Polynomial.roots_prod_x_sub_c
-
+#align polynomial.roots_prod_X_sub_C Polynomial.roots_prod_X_sub_C
+
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(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))) a)) s))) s
+Case conversion may be inaccurate. Consider using '#align polynomial.roots_multiset_prod_X_sub_C Polynomial.roots_multiset_prod_X_sub_Cₓ'. -/
 @[simp]
-theorem roots_multiset_prod_x_sub_c (s : Multiset R) : (s.map fun a => X - C a).Prod.roots = s :=
+theorem roots_multiset_prod_X_sub_C (s : Multiset R) : (s.map fun a => X - C a).Prod.roots = s :=
   by
   rw [roots_multiset_prod, Multiset.bind_map]
   · simp_rw [roots_X_sub_C, Multiset.bind_singleton, Multiset.map_id']
   · rw [Multiset.mem_map]
     rintro ⟨a, -, h⟩
     exact X_sub_C_ne_zero a h
-#align polynomial.roots_multiset_prod_X_sub_C Polynomial.roots_multiset_prod_x_sub_c
-
+#align polynomial.roots_multiset_prod_X_sub_C Polynomial.roots_multiset_prod_X_sub_C
+
+/- warning: polynomial.nat_degree_multiset_prod_X_sub_C_eq_card -> Polynomial.natDegree_multiset_prod_X_sub_C_eq_card is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) s)
+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_multiset_prod_X_sub_C_eq_card Polynomial.natDegree_multiset_prod_X_sub_C_eq_cardₓ'. -/
 @[simp]
-theorem natDegree_multiset_prod_x_sub_c_eq_card (s : Multiset R) :
+theorem natDegree_multiset_prod_X_sub_C_eq_card (s : Multiset R) :
     (s.map fun a => X - C a).Prod.natDegree = s.card :=
   by
   rw [nat_degree_multiset_prod_of_monic, Multiset.map_map]
@@ -743,9 +1121,15 @@ theorem natDegree_multiset_prod_x_sub_c_eq_card (s : Multiset R) :
     simp only [(· ∘ ·), nat_degree_X_sub_C, Multiset.map_const, Multiset.sum_replicate, smul_eq_mul,
       mul_one]
   · exact Multiset.forall_mem_map_iff.2 fun a _ => monic_X_sub_C a
-#align polynomial.nat_degree_multiset_prod_X_sub_C_eq_card Polynomial.natDegree_multiset_prod_x_sub_c_eq_card
-
-theorem card_roots_x_pow_sub_c {n : ℕ} (hn : 0 < n) (a : R) :
+#align polynomial.nat_degree_multiset_prod_X_sub_C_eq_card Polynomial.natDegree_multiset_prod_X_sub_C_eq_card
+
+/- warning: polynomial.card_roots_X_pow_sub_C -> Polynomial.card_roots_X_pow_sub_C is a dubious translation:
+lean 3 declaration is
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+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))] {n : Nat}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) -> (forall (a : R), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R 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+Case conversion may be inaccurate. Consider using '#align polynomial.card_roots_X_pow_sub_C Polynomial.card_roots_X_pow_sub_Cₓ'. -/
+theorem card_roots_X_pow_sub_C {n : ℕ} (hn : 0 < n) (a : R) :
     (roots ((X : R[X]) ^ n - C a)).card ≤ n :=
   WithBot.coe_le_coe.1 <|
     calc
@@ -753,26 +1137,42 @@ theorem card_roots_x_pow_sub_c {n : ℕ} (hn : 0 < n) (a : R) :
         card_roots (X_pow_sub_C_ne_zero hn a)
       _ = n := degree_X_pow_sub_C hn a
       
-#align polynomial.card_roots_X_pow_sub_C Polynomial.card_roots_x_pow_sub_c
+#align polynomial.card_roots_X_pow_sub_C Polynomial.card_roots_X_pow_sub_C
 
 section NthRoots
 
+#print Polynomial.nthRoots /-
 /-- `nth_roots n a` noncomputably returns the solutions to `x ^ n = a`-/
 def nthRoots (n : ℕ) (a : R) : Multiset R :=
   roots ((X : R[X]) ^ n - C a)
 #align polynomial.nth_roots Polynomial.nthRoots
+-/
 
+/- warning: polynomial.mem_nth_roots -> Polynomial.mem_nthRoots 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))] {n : Nat}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n) -> (forall {a : R} {x : R}, Iff (Membership.Mem.{u1, u1} R (Multiset.{u1} R) (Multiset.hasMem.{u1} R) x (Polynomial.nthRoots.{u1} R _inst_1 _inst_2 n a)) (Eq.{succ u1} R (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) x n) a))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.mem_nth_roots Polynomial.mem_nthRootsₓ'. -/
 @[simp]
 theorem mem_nthRoots {n : ℕ} (hn : 0 < n) {a x : R} : x ∈ nthRoots n a ↔ x ^ n = a := by
   rw [nth_roots, mem_roots (X_pow_sub_C_ne_zero hn a), is_root.def, eval_sub, eval_C, eval_pow,
     eval_X, sub_eq_zero]
 #align polynomial.mem_nth_roots Polynomial.mem_nthRoots
 
+#print Polynomial.nthRoots_zero /-
 @[simp]
 theorem nthRoots_zero (r : R) : nthRoots 0 r = 0 := by
   simp only [empty_eq_zero, pow_zero, nth_roots, ← C_1, ← C_sub, roots_C]
 #align polynomial.nth_roots_zero Polynomial.nthRoots_zero
+-/
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.card_nth_roots Polynomial.card_nthRootsₓ'. -/
 theorem card_nthRoots (n : ℕ) (a : R) : (nthRoots n a).card ≤ n :=
   if hn : n = 0 then
     if h : (X : R[X]) ^ n - C a = 0 then by
@@ -788,52 +1188,100 @@ theorem card_nthRoots (n : ℕ) (a : R) : (nthRoots n a).card ≤ n :=
       exact card_roots (X_pow_sub_C_ne_zero (Nat.pos_of_ne_zero hn) a)
 #align polynomial.card_nth_roots Polynomial.card_nthRoots
 
+/- warning: polynomial.nth_roots_two_eq_zero_iff -> Polynomial.nthRoots_two_eq_zero_iff is a dubious translation:
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+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))] {r : R}, Iff (Eq.{succ u1} (Multiset.{u1} R) (Polynomial.nthRoots.{u1} R _inst_1 _inst_2 (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) r) (OfNat.ofNat.{u1} (Multiset.{u1} R) 0 (Zero.toOfNat0.{u1} (Multiset.{u1} R) (Multiset.instZeroMultiset.{u1} R)))) (Not (IsSquare.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) r))
+Case conversion may be inaccurate. Consider using '#align polynomial.nth_roots_two_eq_zero_iff Polynomial.nthRoots_two_eq_zero_iffₓ'. -/
 @[simp]
 theorem nthRoots_two_eq_zero_iff {r : R} : nthRoots 2 r = 0 ↔ ¬IsSquare r := by
   simp_rw [isSquare_iff_exists_sq, eq_zero_iff_forall_not_mem, mem_nth_roots (by norm_num : 0 < 2),
     ← not_exists, eq_comm]
 #align polynomial.nth_roots_two_eq_zero_iff Polynomial.nthRoots_two_eq_zero_iff
 
+#print Polynomial.nthRootsFinset /-
 /-- The multiset `nth_roots ↑n (1 : R)` as a finset. -/
 def nthRootsFinset (n : ℕ) (R : Type _) [CommRing R] [IsDomain R] : Finset R :=
   Multiset.toFinset (nthRoots n (1 : R))
 #align polynomial.nth_roots_finset Polynomial.nthRootsFinset
+-/
 
+/- warning: polynomial.mem_nth_roots_finset -> Polynomial.mem_nthRootsFinset 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.mem_nth_roots_finset Polynomial.mem_nthRootsFinsetₓ'. -/
 @[simp]
 theorem mem_nthRootsFinset {n : ℕ} (h : 0 < n) {x : R} : x ∈ nthRootsFinset n R ↔ x ^ (n : ℕ) = 1 :=
   by rw [nth_roots_finset, mem_to_finset, mem_nth_roots h]
 #align polynomial.mem_nth_roots_finset Polynomial.mem_nthRootsFinset
 
+#print Polynomial.nthRootsFinset_zero /-
 @[simp]
 theorem nthRootsFinset_zero : nthRootsFinset 0 R = ∅ := by simp [nth_roots_finset]
 #align polynomial.nth_roots_finset_zero Polynomial.nthRootsFinset_zero
+-/
 
 end NthRoots
 
+#print Polynomial.Monic.comp /-
 theorem Monic.comp (hp : p.Monic) (hq : q.Monic) (h : q.natDegree ≠ 0) : (p.comp q).Monic := by
   rw [monic.def, leading_coeff_comp h, monic.def.1 hp, monic.def.1 hq, one_pow, one_mul]
 #align polynomial.monic.comp Polynomial.Monic.comp
+-/
 
-theorem Monic.comp_x_add_c (hp : p.Monic) (r : R) : (p.comp (X + C r)).Monic :=
+/- warning: polynomial.monic.comp_X_add_C -> Polynomial.Monic.comp_X_add_C is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.monic.comp_X_add_C Polynomial.Monic.comp_X_add_Cₓ'. -/
+theorem Monic.comp_X_add_C (hp : p.Monic) (r : R) : (p.comp (X + C r)).Monic :=
   by
   refine' hp.comp (monic_X_add_C _) fun ha => _
   rw [nat_degree_X_add_C] at ha
   exact one_ne_zero ha
-#align polynomial.monic.comp_X_add_C Polynomial.Monic.comp_x_add_c
-
-theorem Monic.comp_x_sub_c (hp : p.Monic) (r : R) : (p.comp (X - C r)).Monic := by
+#align polynomial.monic.comp_X_add_C Polynomial.Monic.comp_X_add_C
+
+/- warning: polynomial.monic.comp_X_sub_C -> Polynomial.Monic.comp_X_sub_C is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.monic.comp_X_sub_C Polynomial.Monic.comp_X_sub_Cₓ'. -/
+theorem Monic.comp_X_sub_C (hp : p.Monic) (r : R) : (p.comp (X - C r)).Monic := by
   simpa using hp.comp_X_add_C (-r)
-#align polynomial.monic.comp_X_sub_C Polynomial.Monic.comp_x_sub_c
-
+#align polynomial.monic.comp_X_sub_C Polynomial.Monic.comp_X_sub_C
+
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(CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{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))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (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))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (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} 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+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))] (c : 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))) (Semiring.toMonoidWithZero.{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)))))) (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))) (HSMul.hSMul.{u1, u1, u1} 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))) (instHSMul.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Algebra.toSMul.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.coeff.{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))) (Semiring.toMonoidWithZero.{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))))) c) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) p) (HMul.hMul.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{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))) (Semiring.toMonoidWithZero.{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))))) c) p)
+Case conversion may be inaccurate. Consider using '#align polynomial.units_coeff_zero_smul Polynomial.units_coeff_zero_smulₓ'. -/
 theorem units_coeff_zero_smul (c : R[X]ˣ) (p : R[X]) : (c : R[X]).coeff 0 • p = c * p := by
   rw [← Polynomial.C_mul', ← Polynomial.eq_C_of_degree_eq_zero (degree_coe_units c)]
 #align polynomial.units_coeff_zero_smul Polynomial.units_coeff_zero_smul
 
+/- warning: polynomial.nat_degree_coe_units -> Polynomial.natDegree_coe_units is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_coe_units Polynomial.natDegree_coe_unitsₓ'. -/
 @[simp]
 theorem natDegree_coe_units (u : R[X]ˣ) : natDegree (u : R[X]) = 0 :=
   natDegree_eq_of_degree_eq_some (degree_coe_units u)
 #align polynomial.nat_degree_coe_units Polynomial.natDegree_coe_units
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.comp_eq_zero_iff Polynomial.comp_eq_zero_iffₓ'. -/
 theorem comp_eq_zero_iff : p.comp q = 0 ↔ p = 0 ∨ p.eval (q.coeff 0) = 0 ∧ q = C (q.coeff 0) :=
   by
   constructor
@@ -851,6 +1299,12 @@ theorem comp_eq_zero_iff : p.comp q = 0 ↔ p = 0 ∨ p.eval (q.coeff 0) = 0 ∧
       Or.ndrec (fun h => by rw [h, zero_comp]) (fun h => by rw [h.2, comp_C, h.1, C_0]) h
 #align polynomial.comp_eq_zero_iff Polynomial.comp_eq_zero_iff
 
+/- warning: polynomial.zero_of_eval_zero -> Polynomial.zero_of_eval_zero 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 : Infinite.{succ u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (forall (x : R), Eq.{succ u1} R (Polynomial.eval.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) x p) (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 (CommRing.toRing.{u1} R _inst_1)))))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))
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+Case conversion may be inaccurate. Consider using '#align polynomial.zero_of_eval_zero Polynomial.zero_of_eval_zeroₓ'. -/
 theorem zero_of_eval_zero [Infinite R] (p : R[X]) (h : ∀ x, p.eval x = 0) : p = 0 := by
   classical by_contra hp <;>
       exact
@@ -858,6 +1312,7 @@ theorem zero_of_eval_zero [Infinite R] (p : R[X]) (h : ∀ x, p.eval x = 0) : p
           ⟨p.roots.to_finset, fun x => multiset.mem_to_finset.mpr ((mem_roots hp).mpr (h _))⟩
 #align polynomial.zero_of_eval_zero Polynomial.zero_of_eval_zero
 
+#print Polynomial.funext /-
 theorem funext [Infinite R] {p q : R[X]} (ext : ∀ r : R, p.eval r = q.eval r) : p = q :=
   by
   rw [← sub_eq_zero]
@@ -865,9 +1320,11 @@ theorem funext [Infinite R] {p q : R[X]} (ext : ∀ r : R, p.eval r = q.eval r)
   intro x
   rw [eval_sub, sub_eq_zero, ext]
 #align polynomial.funext Polynomial.funext
+-/
 
 variable [CommRing T]
 
+#print Polynomial.rootSet /-
 /-- The set of distinct roots of `p` in `E`.
 
 If you have a non-separable polynomial, use `polynomial.roots` for the multiset
@@ -875,32 +1332,65 @@ where multiple roots have the appropriate multiplicity. -/
 def rootSet (p : T[X]) (S) [CommRing S] [IsDomain S] [Algebra T S] : Set S :=
   (p.map (algebraMap T S)).roots.toFinset
 #align polynomial.root_set Polynomial.rootSet
+-/
 
+/- warning: polynomial.root_set_def -> Polynomial.rootSet_def is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.root_set_def Polynomial.rootSet_defₓ'. -/
 theorem rootSet_def (p : T[X]) (S) [CommRing S] [IsDomain S] [Algebra T S] :
     p.rootSet S = (p.map (algebraMap T S)).roots.toFinset :=
   rfl
 #align polynomial.root_set_def Polynomial.rootSet_def
 
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+  forall {S : Type.{u1}} {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))] (a : T), Eq.{succ u1} (Set.{u1} S) (Polynomial.rootSet.{u2, u1} T _inst_3 (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} T (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))))) T (fun (_x : T) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : T) => Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} T (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))))) T (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} T (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))))) T (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} T (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))))) T (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u2} T (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3)))))))) (Polynomial.C.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) a) S _inst_4 _inst_5 _inst_6) (EmptyCollection.emptyCollection.{u1} (Set.{u1} S) (Set.instEmptyCollectionSet.{u1} S))
+Case conversion may be inaccurate. Consider using '#align polynomial.root_set_C Polynomial.rootSet_Cₓ'. -/
 @[simp]
-theorem rootSet_c [CommRing S] [IsDomain S] [Algebra T S] (a : T) : (C a).rootSet S = ∅ := by
+theorem rootSet_C [CommRing S] [IsDomain S] [Algebra T S] (a : T) : (C a).rootSet S = ∅ := by
   rw [root_set_def, map_C, roots_C, Multiset.toFinset_zero, Finset.coe_empty]
-#align polynomial.root_set_C Polynomial.rootSet_c
-
+#align polynomial.root_set_C Polynomial.rootSet_C
+
+/- warning: polynomial.root_set_zero -> Polynomial.rootSet_zero is a dubious translation:
+lean 3 declaration is
+  forall {T : Type.{u1}} [_inst_3 : CommRing.{u1} T] (S : Type.{u2}) [_inst_4 : CommRing.{u2} S] [_inst_5 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_6 : Algebra.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))], Eq.{succ u2} (Set.{u2} S) (Polynomial.rootSet.{u1, u2} T _inst_3 (OfNat.ofNat.{u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) 0 (OfNat.mk.{u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) 0 (Zero.zero.{u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) (Polynomial.zero.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3)))))) S _inst_4 _inst_5 _inst_6) (EmptyCollection.emptyCollection.{u2} (Set.{u2} S) (Set.hasEmptyc.{u2} S))
+but is expected to have type
+  forall {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] (S : Type.{u1}) [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))], Eq.{succ u1} (Set.{u1} S) (Polynomial.rootSet.{u2, u1} T _inst_3 (OfNat.ofNat.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Polynomial.zero.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))))) S _inst_4 _inst_5 _inst_6) (EmptyCollection.emptyCollection.{u1} (Set.{u1} S) (Set.instEmptyCollectionSet.{u1} S))
+Case conversion may be inaccurate. Consider using '#align polynomial.root_set_zero Polynomial.rootSet_zeroₓ'. -/
 @[simp]
 theorem rootSet_zero (S) [CommRing S] [IsDomain S] [Algebra T S] : (0 : T[X]).rootSet S = ∅ := by
   rw [← C_0, root_set_C]
 #align polynomial.root_set_zero Polynomial.rootSet_zero
 
+#print Polynomial.rootSetFintype /-
 instance rootSetFintype (p : T[X]) (S : Type _) [CommRing S] [IsDomain S] [Algebra T S] :
     Fintype (p.rootSet S) :=
   FinsetCoe.fintype _
 #align polynomial.root_set_fintype Polynomial.rootSetFintype
+-/
 
+/- warning: polynomial.root_set_finite -> Polynomial.rootSet_finite is a dubious translation:
+lean 3 declaration is
+  forall {T : Type.{u1}} [_inst_3 : CommRing.{u1} T] (p : Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) (S : Type.{u2}) [_inst_4 : CommRing.{u2} S] [_inst_5 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_6 : Algebra.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))], Set.Finite.{u2} S (Polynomial.rootSet.{u1, u2} T _inst_3 p S _inst_4 _inst_5 _inst_6)
+but is expected to have type
+  forall {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] (p : Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (S : Type.{u1}) [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))], Set.Finite.{u1} S (Polynomial.rootSet.{u2, u1} T _inst_3 p S _inst_4 _inst_5 _inst_6)
+Case conversion may be inaccurate. Consider using '#align polynomial.root_set_finite Polynomial.rootSet_finiteₓ'. -/
 theorem rootSet_finite (p : T[X]) (S : Type _) [CommRing S] [IsDomain S] [Algebra T S] :
     (p.rootSet S).Finite :=
   Set.toFinite _
 #align polynomial.root_set_finite Polynomial.rootSet_finite
 
+/- warning: polynomial.bUnion_roots_finite -> Polynomial.bUnion_roots_finite is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_4 : Semiring.{u1} R] [_inst_5 : CommRing.{u2} S] [_inst_6 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5))] (m : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_4) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))) (d : Nat) {U : Set.{u1} R}, (Set.Finite.{u1} R U) -> (Set.Finite.{u2} S (Set.unionᵢ.{u2, succ u1} S (Polynomial.{u1} R _inst_4) (fun (f : Polynomial.{u1} R _inst_4) => Set.unionᵢ.{u2, 0} S (And (LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R _inst_4 f) d) (forall (i : Nat), Membership.Mem.{u1, u1} R (Set.{u1} R) (Set.hasMem.{u1} R) (Polynomial.coeff.{u1} R _inst_4 f i) U)) (fun (hf : And (LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R _inst_4 f) d) (forall (i : Nat), Membership.Mem.{u1, u1} R (Set.{u1} R) (Set.hasMem.{u1} R) (Polynomial.coeff.{u1} R _inst_4 f i) U)) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} S) (Set.{u2} S) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} S) (Set.{u2} S) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} S) (Set.{u2} S) (Finset.Set.hasCoeT.{u2} S))) (Multiset.toFinset.{u2} S (fun (a : S) (b : S) => Classical.propDecidable (Eq.{succ u2} S a b)) (Polynomial.roots.{u2} S _inst_5 _inst_6 (Polynomial.map.{u1, u2} R S _inst_4 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5)) m f)))))))
+but is expected to have type
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_4 : Semiring.{u2} R] [_inst_5 : CommRing.{u1} S] [_inst_6 : IsDomain.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_5))] (m : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_4) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))) (d : Nat) {U : Set.{u2} R}, (Set.Finite.{u2} R U) -> (Set.Finite.{u1} S (Set.unionᵢ.{u1, succ u2} S (Polynomial.{u2} R _inst_4) (fun (f : Polynomial.{u2} R _inst_4) => Set.unionᵢ.{u1, 0} S (And (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u2} R _inst_4 f) d) (forall (i : Nat), Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) (Polynomial.coeff.{u2} R _inst_4 f i) U)) (fun (hf : And (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u2} R _inst_4 f) d) (forall (i : Nat), Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) (Polynomial.coeff.{u2} R _inst_4 f i) U)) => Finset.toSet.{u1} S (Multiset.toFinset.{u1} S (fun (a : S) (b : S) => Classical.propDecidable (Eq.{succ u1} S a b)) (Polynomial.roots.{u1} S _inst_5 _inst_6 (Polynomial.map.{u2, u1} R S _inst_4 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_5)) m f)))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.bUnion_roots_finite Polynomial.bUnion_roots_finiteₓ'. -/
 /-- The set of roots of all polynomials of bounded degree and having coefficients in a finite set
 is finite. -/
 theorem bUnion_roots_finite {R S : Type _} [Semiring R] [CommRing S] [IsDomain S] (m : R →+* S)
@@ -919,23 +1409,47 @@ theorem bUnion_roots_finite {R S : Type _} [Semiring R] [CommRing S] [IsDomain S
     fun i hi => Finset.finite_toSet _
 #align polynomial.bUnion_roots_finite Polynomial.bUnion_roots_finite
 
-theorem mem_root_set' {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Algebra T S] {a : S} :
+/- warning: polynomial.mem_root_set' -> Polynomial.mem_rootSet' is a dubious translation:
+lean 3 declaration is
+  forall {T : Type.{u1}} [_inst_3 : CommRing.{u1} T] {p : Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))} {S : Type.{u2}} [_inst_4 : CommRing.{u2} S] [_inst_5 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_6 : Algebra.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] {a : S}, Iff (Membership.Mem.{u2, u2} S (Set.{u2} S) (Set.hasMem.{u2} S) a (Polynomial.rootSet.{u1, u2} T _inst_3 p S _inst_4 _inst_5 _inst_6)) (And (Ne.{succ u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))) (Polynomial.map.{u1, u2} T S (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (algebraMap.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6) p) (OfNat.ofNat.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))) 0 (OfNat.mk.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))) 0 (Zero.zero.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))) (Polynomial.zero.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))))) (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} T (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) S (CommRing.toCommSemiring.{u1} T _inst_3) (Polynomial.semiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} T T (CommRing.toCommSemiring.{u1} T _inst_3) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Algebra.id.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) (fun (_x : AlgHom.{u1, u1, u2} T (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) S (CommRing.toCommSemiring.{u1} T _inst_3) (Polynomial.semiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} T T (CommRing.toCommSemiring.{u1} T _inst_3) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Algebra.id.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) => (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) -> S) ([anonymous].{u1, u1, u2} T (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) S (CommRing.toCommSemiring.{u1} T _inst_3) (Polynomial.semiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} T T (CommRing.toCommSemiring.{u1} T _inst_3) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Algebra.id.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) (Polynomial.aeval.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6 a) p) (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_4)))))))))))
+but is expected to have type
+  forall {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] {p : Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))} {S : Type.{u1}} [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))] {a : S}, Iff (Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) a (Polynomial.rootSet.{u2, u1} T _inst_3 p S _inst_4 _inst_5 _inst_6)) (And (Ne.{succ u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))) (Polynomial.map.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (algebraMap.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) _inst_6) p) (OfNat.ofNat.{u1} (Polynomial.{u1} S 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(CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6 (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6))))) (Polynomial.aeval.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) _inst_6 a) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (IsDomain.toCancelCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) _inst_4) _inst_5)))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.mem_root_set' Polynomial.mem_rootSet'ₓ'. -/
+theorem mem_rootSet' {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Algebra T S] {a : S} :
     a ∈ p.rootSet S ↔ p.map (algebraMap T S) ≠ 0 ∧ aeval a p = 0 := by
   rw [root_set, Finset.mem_coe, mem_to_finset, mem_roots', is_root.def, ← eval₂_eq_eval_map,
     aeval_def]
-#align polynomial.mem_root_set' Polynomial.mem_root_set'
-
+#align polynomial.mem_root_set' Polynomial.mem_rootSet'
+
+/- warning: polynomial.mem_root_set -> Polynomial.mem_rootSet is a dubious translation:
+lean 3 declaration is
+  forall {T : Type.{u1}} [_inst_3 : CommRing.{u1} T] {p : Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))} {S : Type.{u2}} [_inst_4 : CommRing.{u2} S] [_inst_5 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_6 : Algebra.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_7 : NoZeroSMulDivisors.{u1, u2} T S (MulZeroClass.toHasZero.{u1} T (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} T (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} T (NonAssocRing.toNonUnitalNonAssocRing.{u1} T (Ring.toNonAssocRing.{u1} T (CommRing.toRing.{u1} T _inst_3)))))) (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_4)))))) (SMulZeroClass.toHasSmul.{u1, u2} T S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} T S (MulZeroClass.toHasZero.{u1} T (MulZeroOneClass.toMulZeroClass.{u1} T (MonoidWithZero.toMulZeroOneClass.{u1} T (Semiring.toMonoidWithZero.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} T S (Semiring.toMonoidWithZero.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) (Module.toMulActionWithZero.{u1, u2} T S (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))) (Algebra.toModule.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6)))))] {a : S}, Iff (Membership.Mem.{u2, u2} S (Set.{u2} S) (Set.hasMem.{u2} S) a (Polynomial.rootSet.{u1, u2} T _inst_3 p S _inst_4 _inst_5 _inst_6)) (And (Ne.{succ u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) p (OfNat.ofNat.{u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) 0 (OfNat.mk.{u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) 0 (Zero.zero.{u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) (Polynomial.zero.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))))))) (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} T (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) S (CommRing.toCommSemiring.{u1} T _inst_3) (Polynomial.semiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} T T (CommRing.toCommSemiring.{u1} T _inst_3) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Algebra.id.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) (fun (_x : AlgHom.{u1, u1, u2} T (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) S (CommRing.toCommSemiring.{u1} T _inst_3) (Polynomial.semiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} T T (CommRing.toCommSemiring.{u1} T _inst_3) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Algebra.id.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) => (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) -> S) ([anonymous].{u1, u1, u2} T (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) S (CommRing.toCommSemiring.{u1} T _inst_3) (Polynomial.semiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} T T (CommRing.toCommSemiring.{u1} T _inst_3) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Algebra.id.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) (Polynomial.aeval.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6 a) p) (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_4)))))))))))
+but is expected to have type
+  forall {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] {p : Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))} {S : Type.{u1}} [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))] [_inst_7 : NoZeroSMulDivisors.{u2, u1} T S (CommMonoidWithZero.toZero.{u2} T (CommSemiring.toCommMonoidWithZero.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommMonoidWithZero.toZero.{u1} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} S (IsDomain.toCancelCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4) _inst_5))) (Algebra.toSMul.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) _inst_6)] {a : S}, Iff (Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) a (Polynomial.rootSet.{u2, u1} T _inst_3 p S _inst_4 _inst_5 _inst_6)) (And (Ne.{succ u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) p (OfNat.ofNat.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Polynomial.zero.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3)))))) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (fun (_x : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (SMulZeroClass.toSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toZero.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (SMulZeroClass.toSMul.{u2, u1} T S (AddMonoid.toZero.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))))))) (DistribSMul.toSMulZeroClass.{u2, u1} T S (AddMonoid.toAddZeroClass.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))))))) (DistribMulAction.toDistribSMul.{u2, u1} T S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)))))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6 (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6))))) (Polynomial.aeval.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) _inst_6 a) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (IsDomain.toCancelCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) _inst_4) _inst_5)))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.mem_root_set Polynomial.mem_rootSetₓ'. -/
 theorem mem_rootSet {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Algebra T S]
     [NoZeroSMulDivisors T S] {a : S} : a ∈ p.rootSet S ↔ p ≠ 0 ∧ aeval a p = 0 := by
   rw [mem_root_set',
     (map_injective _ (NoZeroSMulDivisors.algebraMap_injective T S)).ne_iff' (Polynomial.map_zero _)]
 #align polynomial.mem_root_set Polynomial.mem_rootSet
 
+/- warning: polynomial.mem_root_set_of_ne -> Polynomial.mem_rootSet_of_ne is a dubious translation:
+lean 3 declaration is
+  forall {T : Type.{u1}} [_inst_3 : CommRing.{u1} T] {p : Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))} {S : Type.{u2}} [_inst_4 : CommRing.{u2} S] [_inst_5 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_6 : Algebra.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_7 : NoZeroSMulDivisors.{u1, u2} T S (MulZeroClass.toHasZero.{u1} T (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} T (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} T (NonAssocRing.toNonUnitalNonAssocRing.{u1} T (Ring.toNonAssocRing.{u1} T (CommRing.toRing.{u1} T _inst_3)))))) (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_4)))))) (SMulZeroClass.toHasSmul.{u1, u2} T S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} T S (MulZeroClass.toHasZero.{u1} T (MulZeroOneClass.toMulZeroClass.{u1} T (MonoidWithZero.toMulZeroOneClass.{u1} T (Semiring.toMonoidWithZero.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} T S (Semiring.toMonoidWithZero.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) (Module.toMulActionWithZero.{u1, u2} T S (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))) (Algebra.toModule.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6)))))], (Ne.{succ u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) p (OfNat.ofNat.{u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) 0 (OfNat.mk.{u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) 0 (Zero.zero.{u1} (Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))) (Polynomial.zero.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))))))) -> (forall {a : S}, Iff (Membership.Mem.{u2, u2} S (Set.{u2} S) (Set.hasMem.{u2} S) a (Polynomial.rootSet.{u1, u2} T _inst_3 p S _inst_4 _inst_5 _inst_6)) (Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} T (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) S (CommRing.toCommSemiring.{u1} T _inst_3) (Polynomial.semiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} T T (CommRing.toCommSemiring.{u1} T _inst_3) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Algebra.id.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) (fun (_x : AlgHom.{u1, u1, u2} T (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) S (CommRing.toCommSemiring.{u1} T _inst_3) (Polynomial.semiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} T T (CommRing.toCommSemiring.{u1} T _inst_3) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Algebra.id.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) => (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) -> S) ([anonymous].{u1, u1, u2} T (Polynomial.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) S (CommRing.toCommSemiring.{u1} T _inst_3) (Polynomial.semiring.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} T T (CommRing.toCommSemiring.{u1} T _inst_3) (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (Algebra.id.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) _inst_6) (Polynomial.aeval.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6 a) p) (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_4)))))))))))
+but is expected to have type
+  forall {T : Type.{u2}} [_inst_3 : CommRing.{u2} T] {p : Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))} {S : Type.{u1}} [_inst_4 : CommRing.{u1} S] [_inst_5 : IsDomain.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))] [_inst_6 : Algebra.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))] [_inst_7 : NoZeroSMulDivisors.{u2, u1} T S (CommMonoidWithZero.toZero.{u2} T (CommSemiring.toCommMonoidWithZero.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommMonoidWithZero.toZero.{u1} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} S (IsDomain.toCancelCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_4) _inst_5))) (Algebra.toSMul.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) _inst_6)], (Ne.{succ u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) p (OfNat.ofNat.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3))) (Polynomial.zero.{u2} T (Ring.toSemiring.{u2} T (CommRing.toRing.{u2} T _inst_3)))))) -> (forall {a : S}, Iff (Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) a (Polynomial.rootSet.{u2, u1} T _inst_3 p S _inst_4 _inst_5 _inst_6)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (fun (_x : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) => S) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) _inst_6) T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (SMulZeroClass.toSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toZero.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))))))) (Module.toDistribMulAction.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))) (Algebra.toModule.{u2, u2} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (CommRing.toCommSemiring.{u2} T _inst_3) (Polynomial.semiring.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} T T (CommRing.toCommSemiring.{u2} T _inst_3) (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (Algebra.id.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))))))) (SMulZeroClass.toSMul.{u2, u1} T S (AddMonoid.toZero.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))))))) (DistribSMul.toSMulZeroClass.{u2, u1} T S (AddMonoid.toAddZeroClass.{u1} S (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))))))) (DistribMulAction.toDistribSMul.{u2, u1} T S (MonoidWithZero.toMonoid.{u2} T (Semiring.toMonoidWithZero.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u1} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)))))) (Module.toDistribMulAction.{u2, u1} T S (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4))))) (Algebra.toModule.{u2, u1} T S (CommRing.toCommSemiring.{u2} T _inst_3) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_4)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} T (Polynomial.{u2} T (CommSemiring.toSemiring.{u2} T (CommRing.toCommSemiring.{u2} T _inst_3))) S (CommRing.toCommSemiring.{u2} T _inst_3) 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+Case conversion may be inaccurate. Consider using '#align polynomial.mem_root_set_of_ne Polynomial.mem_rootSet_of_neₓ'. -/
 theorem mem_rootSet_of_ne {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Algebra T S]
     [NoZeroSMulDivisors T S] (hp : p ≠ 0) {a : S} : a ∈ p.rootSet S ↔ aeval a p = 0 :=
   mem_rootSet.trans <| and_iff_right hp
 #align polynomial.mem_root_set_of_ne Polynomial.mem_rootSet_of_ne
 
+/- warning: polynomial.root_set_maps_to' -> Polynomial.rootSet_maps_to' is a dubious translation:
+lean 3 declaration is
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(CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))) (Algebra.toModule.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6))))) (SMulZeroClass.toSMul.{u3, u1} T S' (AddMonoid.toZero.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7))))))) (DistribSMul.toSMulZeroClass.{u3, u1} T S' (AddMonoid.toAddZeroClass.{u1} S' (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7))))))) (DistribMulAction.toDistribSMul.{u3, u1} T S' (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)))))) (Module.toDistribMulAction.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7))))) (Algebra.toModule.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_6 _inst_9) T S S' (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))) (AddCommMonoid.toAddMonoid.{u1} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)))))) (Module.toDistribMulAction.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))) (Algebra.toModule.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6)) (Module.toDistribMulAction.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7))))) (Algebra.toModule.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_9)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_6 _inst_9) T S S' (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)))) (Module.toDistribMulAction.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))) (Algebra.toModule.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6)) (Module.toDistribMulAction.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7))))) (Algebra.toModule.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_9)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_6 _inst_9 (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_6 _inst_9) (AlgHom.algHomClass.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_6 _inst_9))))) f) (Polynomial.rootSet.{u3, u2} T _inst_3 p S _inst_4 _inst_5 _inst_6) (Polynomial.rootSet.{u3, u1} T _inst_3 p S' _inst_7 _inst_8 _inst_9))
+Case conversion may be inaccurate. Consider using '#align polynomial.root_set_maps_to' Polynomial.rootSet_maps_to'ₓ'. -/
 theorem rootSet_maps_to' {p : T[X]} {S S'} [CommRing S] [IsDomain S] [Algebra T S] [CommRing S']
     [IsDomain S'] [Algebra T S'] (hp : p.map (algebraMap T S') = 0 → p.map (algebraMap T S) = 0)
     (f : S →ₐ[T] S') : (p.rootSet S).MapsTo f (p.rootSet S') := fun x hx =>
@@ -945,15 +1459,25 @@ theorem rootSet_maps_to' {p : T[X]} {S S'} [CommRing S] [IsDomain S] [Algebra T
   exact ⟨mt hp hx.1, rfl⟩
 #align polynomial.root_set_maps_to' Polynomial.rootSet_maps_to'
 
+#print Polynomial.ne_zero_of_mem_rootSet /-
 theorem ne_zero_of_mem_rootSet {p : T[X]} [CommRing S] [IsDomain S] [Algebra T S] {a : S}
     (h : a ∈ p.rootSet S) : p ≠ 0 := fun hf => by rwa [hf, root_set_zero] at h
 #align polynomial.ne_zero_of_mem_root_set Polynomial.ne_zero_of_mem_rootSet
+-/
 
+#print Polynomial.aeval_eq_zero_of_mem_rootSet /-
 theorem aeval_eq_zero_of_mem_rootSet {p : T[X]} [CommRing S] [IsDomain S] [Algebra T S] {a : S}
     (hx : a ∈ p.rootSet S) : aeval a p = 0 :=
-  (mem_root_set'.1 hx).2
+  (mem_rootSet'.1 hx).2
 #align polynomial.aeval_eq_zero_of_mem_root_set Polynomial.aeval_eq_zero_of_mem_rootSet
+-/
 
+/- warning: polynomial.root_set_maps_to -> Polynomial.rootSet_mapsTo is a dubious translation:
+lean 3 declaration is
+  forall {T : Type.{u1}} [_inst_3 : CommRing.{u1} T] {p : Polynomial.{u1} T (Ring.toSemiring.{u1} T (CommRing.toRing.{u1} T _inst_3))} {S : Type.{u2}} {S' : Type.{u3}} [_inst_4 : CommRing.{u2} S] [_inst_5 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_6 : Algebra.{u1, u2} T S (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_7 : CommRing.{u3} S'] [_inst_8 : IsDomain.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7))] [_inst_9 : Algebra.{u1, u3} T S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7))] [_inst_10 : NoZeroSMulDivisors.{u1, u3} T S' (MulZeroClass.toHasZero.{u1} T (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} T (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} T (NonAssocRing.toNonUnitalNonAssocRing.{u1} T (Ring.toNonAssocRing.{u1} T (CommRing.toRing.{u1} T _inst_3)))))) (MulZeroClass.toHasZero.{u3} S' (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} S' (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} S' (NonAssocRing.toNonUnitalNonAssocRing.{u3} S' (Ring.toNonAssocRing.{u3} S' (CommRing.toRing.{u3} S' _inst_7)))))) (SMulZeroClass.toHasSmul.{u1, u3} T S' (AddZeroClass.toHasZero.{u3} S' (AddMonoid.toAddZeroClass.{u3} S' (AddCommMonoid.toAddMonoid.{u3} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S' (Semiring.toNonAssocSemiring.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} T S' (MulZeroClass.toHasZero.{u1} T (MulZeroOneClass.toMulZeroClass.{u1} T (MonoidWithZero.toMulZeroOneClass.{u1} T (Semiring.toMonoidWithZero.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)))))) (AddZeroClass.toHasZero.{u3} S' (AddMonoid.toAddZeroClass.{u3} S' (AddCommMonoid.toAddMonoid.{u3} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S' (Semiring.toNonAssocSemiring.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} T S' (Semiring.toMonoidWithZero.{u1} T (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3))) (AddZeroClass.toHasZero.{u3} S' (AddMonoid.toAddZeroClass.{u3} S' (AddCommMonoid.toAddMonoid.{u3} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S' (Semiring.toNonAssocSemiring.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)))))))) (Module.toMulActionWithZero.{u1, u3} T S' (CommSemiring.toSemiring.{u1} T (CommRing.toCommSemiring.{u1} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S' (Semiring.toNonAssocSemiring.{u3} S' (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7))))) (Algebra.toModule.{u1, u3} T S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)) _inst_9)))))] (f : AlgHom.{u1, u2, u3} T S S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)) _inst_6 _inst_9), Set.MapsTo.{u2, u3} S S' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} T S S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)) _inst_6 _inst_9) (fun (_x : AlgHom.{u1, u2, u3} T S S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)) _inst_6 _inst_9) => S -> S') ([anonymous].{u1, u2, u3} T S S' (CommRing.toCommSemiring.{u1} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u3} S' (CommRing.toRing.{u3} S' _inst_7)) _inst_6 _inst_9) f) (Polynomial.rootSet.{u1, u2} T _inst_3 p S _inst_4 _inst_5 _inst_6) (Polynomial.rootSet.{u1, u3} T _inst_3 p S' _inst_7 _inst_8 _inst_9)
+but is expected to have type
+  forall {T : Type.{u3}} [_inst_3 : CommRing.{u3} T] {p : Polynomial.{u3} T (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_3))} {S : Type.{u2}} {S' : Type.{u1}} [_inst_4 : CommRing.{u2} S] [_inst_5 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_6 : Algebra.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_7 : CommRing.{u1} S'] [_inst_8 : IsDomain.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7))] [_inst_9 : Algebra.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7))] [_inst_10 : NoZeroSMulDivisors.{u3, u1} T S' (CommMonoidWithZero.toZero.{u3} T (CommSemiring.toCommMonoidWithZero.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3))) (CommMonoidWithZero.toZero.{u1} S' (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} S' (IsDomain.toCancelCommMonoidWithZero.{u1} S' (CommRing.toCommSemiring.{u1} S' _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_9)] (f : AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_6 _inst_9), Set.MapsTo.{u2, u1} S S' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_6 _inst_9) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => S') _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_6 _inst_9) T S S' (SMulZeroClass.toSMul.{u3, u2} T S (AddMonoid.toZero.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))))) (DistribSMul.toSMulZeroClass.{u3, u2} T S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))))) (DistribMulAction.toDistribSMul.{u3, u2} T S (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S 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(CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_6 _inst_9) T S S' (MonoidWithZero.toMonoid.{u3} T (Semiring.toMonoidWithZero.{u3} T (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)))) (Module.toDistribMulAction.{u3, u2} T S (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))) (Algebra.toModule.{u3, u2} T S (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_6)) (Module.toDistribMulAction.{u3, u1} T S' (CommSemiring.toSemiring.{u3} T (CommRing.toCommSemiring.{u3} T _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S' (Semiring.toNonAssocSemiring.{u1} S' (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7))))) (Algebra.toModule.{u3, u1} T S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_9)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_6 _inst_9 (AlgHom.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_6 _inst_9) (AlgHom.algHomClass.{u3, u2, u1} T S S' (CommRing.toCommSemiring.{u3} T _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) (Ring.toSemiring.{u1} S' (CommRing.toRing.{u1} S' _inst_7)) _inst_6 _inst_9))))) f) (Polynomial.rootSet.{u3, u2} T _inst_3 p S _inst_4 _inst_5 _inst_6) (Polynomial.rootSet.{u3, u1} T _inst_3 p S' _inst_7 _inst_8 _inst_9)
+Case conversion may be inaccurate. Consider using '#align polynomial.root_set_maps_to Polynomial.rootSet_mapsToₓ'. -/
 theorem rootSet_mapsTo {p : T[X]} {S S'} [CommRing S] [IsDomain S] [Algebra T S] [CommRing S']
     [IsDomain S'] [Algebra T S'] [NoZeroSMulDivisors T S'] (f : S →ₐ[T] S') :
     (p.rootSet S).MapsTo f (p.rootSet S') :=
@@ -966,6 +1490,12 @@ theorem rootSet_mapsTo {p : T[X]} {S S'} [CommRing S] [IsDomain S] [Algebra T S]
 
 end Roots
 
+/- warning: polynomial.coeff_coe_units_zero_ne_zero -> Polynomial.coeff_coe_units_zero_ne_zero is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align polynomial.coeff_coe_units_zero_ne_zero Polynomial.coeff_coe_units_zero_ne_zeroₓ'. -/
 theorem coeff_coe_units_zero_ne_zero (u : R[X]ˣ) : coeff (u : R[X]) 0 ≠ 0 :=
   by
   conv in 0 => rw [← nat_degree_coe_units u]
@@ -973,12 +1503,24 @@ theorem coeff_coe_units_zero_ne_zero (u : R[X]ˣ) : coeff (u : R[X]) 0 ≠ 0 :=
   exact Units.ne_zero _
 #align polynomial.coeff_coe_units_zero_ne_zero Polynomial.coeff_coe_units_zero_ne_zero
 
+/- warning: polynomial.degree_eq_degree_of_associated -> Polynomial.degree_eq_degree_of_associated is a dubious translation:
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+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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Associated.{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))) (Semiring.toMonoidWithZero.{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))))) p q) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) q))
+Case conversion may be inaccurate. Consider using '#align polynomial.degree_eq_degree_of_associated Polynomial.degree_eq_degree_of_associatedₓ'. -/
 theorem degree_eq_degree_of_associated (h : Associated p q) : degree p = degree q :=
   by
   let ⟨u, hu⟩ := h
   simp [hu.symm]
 #align polynomial.degree_eq_degree_of_associated Polynomial.degree_eq_degree_of_associated
 
+/- warning: polynomial.degree_eq_one_of_irreducible_of_root -> Polynomial.degree_eq_one_of_irreducible_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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p) -> (forall {x : R}, (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p x) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{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))))))
+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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Irreducible.{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))) (Semiring.toMonoidWithZero.{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))))) p) -> (forall {x : R}, (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p x) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) (OfNat.ofNat.{0} (WithBot.{0} Nat) 1 (One.toOfNat1.{0} (WithBot.{0} Nat) (WithBot.one.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.degree_eq_one_of_irreducible_of_root Polynomial.degree_eq_one_of_irreducible_of_rootₓ'. -/
 theorem degree_eq_one_of_irreducible_of_root (hi : Irreducible p) {x : R} (hx : IsRoot p x) :
     degree p = 1 :=
   let ⟨g, hg⟩ := dvd_iff_isRoot.2 hx
@@ -991,6 +1533,7 @@ theorem degree_eq_one_of_irreducible_of_root (hi : Irreducible p) {x : R} (hx :
     fun hgu => by rw [hg, degree_mul, degree_X_sub_C, degree_eq_zero_of_is_unit hgu, add_zero]
 #align polynomial.degree_eq_one_of_irreducible_of_root Polynomial.degree_eq_one_of_irreducible_of_root
 
+#print Polynomial.leadingCoeff_divByMonic_of_monic /-
 /-- Division by a monic polynomial doesn't change the leading coefficient. -/
 theorem leadingCoeff_divByMonic_of_monic {R : Type u} [CommRing R] {p q : R[X]} (hmonic : q.Monic)
     (hdegree : q.degree ≤ p.degree) : (p /ₘ q).leadingCoeff = p.leadingCoeff :=
@@ -1004,8 +1547,15 @@ theorem leadingCoeff_divByMonic_of_monic {R : Type u} [CommRing R] {p q : R[X]}
   rw [degree_mul' h, degree_add_div_by_monic hmonic hdegree]
   exact (degree_mod_by_monic_lt p hmonic).trans_le hdegree
 #align polynomial.leading_coeff_div_by_monic_of_monic Polynomial.leadingCoeff_divByMonic_of_monic
+-/
 
-theorem leadingCoeff_divByMonic_x_sub_c (p : R[X]) (hp : degree p ≠ 0) (a : R) :
+/- warning: polynomial.leading_coeff_div_by_monic_X_sub_C -> Polynomial.leadingCoeff_divByMonic_X_sub_C 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))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Ne.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{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))))) -> (forall (a : R), Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.divByMonic.{u1} R (CommRing.toRing.{u1} R _inst_1) p (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)))) (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))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Ne.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{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))))) -> (forall (a : R), Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.divByMonic.{u1} R (CommRing.toRing.{u1} R _inst_1) p (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R 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+Case conversion may be inaccurate. Consider using '#align polynomial.leading_coeff_div_by_monic_X_sub_C Polynomial.leadingCoeff_divByMonic_X_sub_Cₓ'. -/
+theorem leadingCoeff_divByMonic_X_sub_C (p : R[X]) (hp : degree p ≠ 0) (a : R) :
     leadingCoeff (p /ₘ (X - C a)) = leadingCoeff p :=
   by
   nontriviality
@@ -1013,8 +1563,14 @@ theorem leadingCoeff_divByMonic_x_sub_c (p : R[X]) (hp : degree p ≠ 0) (a : R)
   · rw [degree_eq_bot.mp <| (Nat.WithBot.lt_zero_iff _).mp hd, zero_div_by_monic]
   refine' leading_coeff_div_by_monic_of_monic (monic_X_sub_C a) _
   rwa [degree_X_sub_C, Nat.WithBot.one_le_iff_zero_lt]
-#align polynomial.leading_coeff_div_by_monic_X_sub_C Polynomial.leadingCoeff_divByMonic_x_sub_c
-
+#align polynomial.leading_coeff_div_by_monic_X_sub_C Polynomial.leadingCoeff_divByMonic_X_sub_C
+
+/- warning: polynomial.eq_leading_coeff_mul_of_monic_of_dvd_of_nat_degree_le -> Polynomial.eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) p) -> (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.commRing.{u1} R _inst_3))))))) p q) -> (LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) q) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) p)) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) q (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) q)) p))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) p) -> (Dvd.dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.commRing.{u1} R _inst_3))))))) p q) -> (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) q) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) p)) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) q (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) q)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) q)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) q)) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) 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_3))) _x) (MulHomClass.toFunLike.{u1, u1, u1} 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(CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) q)) p))
+Case conversion may be inaccurate. Consider using '#align polynomial.eq_leading_coeff_mul_of_monic_of_dvd_of_nat_degree_le Polynomial.eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_leₓ'. -/
 theorem eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le {R} [CommRing R] {p q : R[X]}
     (hp : p.Monic) (hdiv : p ∣ q) (hdeg : q.natDegree ≤ p.natDegree) : q = C q.leadingCoeff * p :=
   by
@@ -1031,39 +1587,71 @@ theorem eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le {R} [CommRing R] {p
   · exact (add_right_inj _).1 (le_antisymm hdeg <| Nat.le.intro rfl)
 #align polynomial.eq_leading_coeff_mul_of_monic_of_dvd_of_nat_degree_le Polynomial.eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le
 
+#print Polynomial.eq_of_monic_of_dvd_of_natDegree_le /-
 theorem eq_of_monic_of_dvd_of_natDegree_le {R} [CommRing R] {p q : R[X]} (hp : p.Monic)
     (hq : q.Monic) (hdiv : p ∣ q) (hdeg : q.natDegree ≤ p.natDegree) : q = p :=
   by
   convert eq_leading_coeff_mul_of_monic_of_dvd_of_nat_degree_le hp hdiv hdeg
   rw [hq.leading_coeff, C_1, one_mul]
 #align polynomial.eq_of_monic_of_dvd_of_nat_degree_le Polynomial.eq_of_monic_of_dvd_of_natDegree_le
+-/
 
-theorem isCoprime_x_sub_c_of_isUnit_sub {R} [CommRing R] {a b : R} (h : IsUnit (a - b)) :
+/- warning: polynomial.is_coprime_X_sub_C_of_is_unit_sub -> Polynomial.isCoprime_X_sub_C_of_isUnit_sub is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {a : R} {b : R}, (IsUnit.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_3)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))))) a b)) -> (IsCoprime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) a)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) b)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {a : R} {b : R}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_3))) a b)) -> (IsCoprime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} 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+Case conversion may be inaccurate. Consider using '#align polynomial.is_coprime_X_sub_C_of_is_unit_sub Polynomial.isCoprime_X_sub_C_of_isUnit_subₓ'. -/
+theorem isCoprime_X_sub_C_of_isUnit_sub {R} [CommRing R] {a b : R} (h : IsUnit (a - b)) :
     IsCoprime (X - C a) (X - C b) :=
   ⟨-C h.Unit⁻¹.val, C h.Unit⁻¹.val,
     by
     rw [neg_mul_comm, ← left_distrib, neg_add_eq_sub, sub_sub_sub_cancel_left, ← C_sub, ← C_mul]
     convert C_1
     exact h.coe_inv_mul⟩
-#align polynomial.is_coprime_X_sub_C_of_is_unit_sub Polynomial.isCoprime_x_sub_c_of_isUnit_sub
-
-theorem pairwise_coprime_x_sub_c {K} [Field K] {I : Type v} {s : I → K} (H : Function.Injective s) :
+#align polynomial.is_coprime_X_sub_C_of_is_unit_sub Polynomial.isCoprime_X_sub_C_of_isUnit_sub
+
+/- warning: polynomial.pairwise_coprime_X_sub_C -> Polynomial.pairwise_coprime_X_sub_C is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u2}} [_inst_3 : Field.{u2} K] {I : Type.{u1}} {s : I -> K}, (Function.Injective.{succ u1, succ u2} I K s) -> (Pairwise.{u1} I (Function.onFun.{succ u1, succ u2, 1} I (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) Prop (IsCoprime.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (Polynomial.commSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_3)))) (fun (i : I) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (instHSub.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (Polynomial.sub.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (Polynomial.X.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))))) (fun (_x : RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))))) => K -> (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) (RingHom.hasCoeToFun.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))))) (Polynomial.C.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (s i)))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.pairwise_coprime_X_sub_C Polynomial.pairwise_coprime_X_sub_Cₓ'. -/
+theorem pairwise_coprime_X_sub_C {K} [Field K] {I : Type v} {s : I → K} (H : Function.Injective s) :
     Pairwise (IsCoprime on fun i : I => X - C (s i)) := fun i j hij =>
-  isCoprime_x_sub_c_of_isUnit_sub (sub_ne_zero_of_ne <| H.Ne hij).IsUnit
-#align polynomial.pairwise_coprime_X_sub_C Polynomial.pairwise_coprime_x_sub_c
-
-theorem monic_prod_multiset_x_sub_c : Monic (p.roots.map fun a => X - C a).Prod :=
+  isCoprime_X_sub_C_of_isUnit_sub (sub_ne_zero_of_ne <| H.Ne hij).IsUnit
+#align polynomial.pairwise_coprime_X_sub_C Polynomial.pairwise_coprime_X_sub_C
+
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+Case conversion may be inaccurate. Consider using '#align polynomial.monic_prod_multiset_X_sub_C Polynomial.monic_prod_multiset_X_sub_Cₓ'. -/
+theorem monic_prod_multiset_X_sub_C : Monic (p.roots.map fun a => X - C a).Prod :=
   monic_multiset_prod_of_monic _ _ fun a _ => monic_X_sub_C a
-#align polynomial.monic_prod_multiset_X_sub_C Polynomial.monic_prod_multiset_x_sub_c
-
+#align polynomial.monic_prod_multiset_X_sub_C Polynomial.monic_prod_multiset_X_sub_C
+
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_inst_2 p)) (fun (a : R) => HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R 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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))) a)) (Polynomial.rootMultiplicity.{u1} R _inst_1 a p)))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.prod_multiset_root_eq_finset_root Polynomial.prod_multiset_root_eq_finset_rootₓ'. -/
 theorem prod_multiset_root_eq_finset_root :
     (p.roots.map fun a => X - C a).Prod =
       p.roots.toFinset.Prod fun a => (X - C a) ^ rootMultiplicity a p :=
   by simp only [count_roots, Finset.prod_multiset_map_count]
 #align polynomial.prod_multiset_root_eq_finset_root Polynomial.prod_multiset_root_eq_finset_root
 
+/- warning: polynomial.prod_multiset_X_sub_C_dvd -> Polynomial.prod_multiset_X_sub_C_dvd 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))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 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))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), Dvd.dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))) p
+Case conversion may be inaccurate. Consider using '#align polynomial.prod_multiset_X_sub_C_dvd Polynomial.prod_multiset_X_sub_C_dvdₓ'. -/
 /-- The product `∏ (X - a)` for `a` inside the multiset `p.roots` divides `p`. -/
-theorem prod_multiset_x_sub_c_dvd (p : R[X]) : (p.roots.map fun a => X - C a).Prod ∣ p :=
+theorem prod_multiset_X_sub_C_dvd (p : R[X]) : (p.roots.map fun a => X - C a).Prod ∣ p :=
   by
   rw [← map_dvd_map _ (IsFractionRing.injective R <| FractionRing R) monic_prod_multiset_X_sub_C]
   rw [prod_multiset_root_eq_finset_root, Polynomial.map_prod]
@@ -1071,10 +1659,16 @@ theorem prod_multiset_x_sub_c_dvd (p : R[X]) : (p.roots.map fun a => X - C a).Pr
   · simp_rw [Polynomial.map_pow, Polynomial.map_sub, map_C, map_X]
     exact (pairwise_coprime_X_sub_C (IsFractionRing.injective R <| FractionRing R) h).pow
   · exact Polynomial.map_dvd _ (pow_root_multiplicity_dvd p a)
-#align polynomial.prod_multiset_X_sub_C_dvd Polynomial.prod_multiset_x_sub_c_dvd
-
+#align polynomial.prod_multiset_X_sub_C_dvd Polynomial.prod_multiset_X_sub_C_dvd
+
+/- warning: multiset.prod_X_sub_C_dvd_iff_le_roots -> Multiset.prod_X_sub_C_dvd_iff_le_roots 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (forall (s : Multiset.{u1} R), Iff (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) s)) p) (LE.le.{u1} (Multiset.{u1} R) (Preorder.toLE.{u1} (Multiset.{u1} R) (PartialOrder.toPreorder.{u1} (Multiset.{u1} R) (Multiset.partialOrder.{u1} R))) s (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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) -> (forall (s : Multiset.{u1} R), Iff (Dvd.dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} 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(Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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} 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(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))) a)) s)) p) (LE.le.{u1} (Multiset.{u1} R) (Preorder.toLE.{u1} (Multiset.{u1} R) (PartialOrder.toPreorder.{u1} (Multiset.{u1} R) (Multiset.instPartialOrderMultiset.{u1} R))) s (Polynomial.roots.{u1} R _inst_1 _inst_2 p)))
+Case conversion may be inaccurate. Consider using '#align multiset.prod_X_sub_C_dvd_iff_le_roots Multiset.prod_X_sub_C_dvd_iff_le_rootsₓ'. -/
 /-- A Galois connection. -/
-theorem Multiset.prod_x_sub_c_dvd_iff_le_roots {p : R[X]} (hp : p ≠ 0) (s : Multiset R) :
+theorem Multiset.prod_X_sub_C_dvd_iff_le_roots {p : R[X]} (hp : p ≠ 0) (s : Multiset R) :
     (s.map fun a => X - C a).Prod ∣ p ↔ s ≤ p.roots :=
   ⟨fun h =>
     Multiset.le_iff_count.2 fun r =>
@@ -1083,10 +1677,16 @@ theorem Multiset.prod_x_sub_c_dvd_iff_le_roots {p : R[X]} (hp : p ≠ 0) (s : Mu
         Multiset.map_replicate fun a => X - C a, ← Multiset.filter_eq]
       exact (Multiset.prod_dvd_prod_of_le <| Multiset.map_le_map <| s.filter_le _).trans h,
     fun h =>
-    (Multiset.prod_dvd_prod_of_le <| Multiset.map_le_map h).trans p.prod_multiset_x_sub_c_dvd⟩
-#align multiset.prod_X_sub_C_dvd_iff_le_roots Multiset.prod_x_sub_c_dvd_iff_le_roots
-
-theorem exists_prod_multiset_x_sub_c_mul (p : R[X]) :
+    (Multiset.prod_dvd_prod_of_le <| Multiset.map_le_map h).trans p.prod_multiset_X_sub_C_dvd⟩
+#align multiset.prod_X_sub_C_dvd_iff_le_roots Multiset.prod_X_sub_C_dvd_iff_le_roots
+
+/- warning: polynomial.exists_prod_multiset_X_sub_C_mul -> Polynomial.exists_prod_multiset_X_sub_C_mul 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))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), Exists.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => And (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} 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+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))] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), Exists.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => And (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} 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_inst_1 _inst_2 p))) q) p) (And (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) instAddNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) q)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) (Eq.{succ u1} (Multiset.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 q) (OfNat.ofNat.{u1} (Multiset.{u1} R) 0 (Zero.toOfNat0.{u1} (Multiset.{u1} R) (Multiset.instZeroMultiset.{u1} R))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.exists_prod_multiset_X_sub_C_mul Polynomial.exists_prod_multiset_X_sub_C_mulₓ'. -/
+theorem exists_prod_multiset_X_sub_C_mul (p : R[X]) :
     ∃ q,
       (p.roots.map fun a => X - C a).Prod * q = p ∧
         p.roots.card + q.natDegree = p.natDegree ∧ q.roots = 0 :=
@@ -1103,25 +1703,37 @@ theorem exists_prod_multiset_x_sub_c_mul (p : R[X]) :
   · replace he := congr_arg roots he.symm
     rw [roots_mul, roots_multiset_prod_X_sub_C] at he
     exacts[add_right_eq_self.1 he, mul_ne_zero monic_prod_multiset_X_sub_C.ne_zero hq]
-#align polynomial.exists_prod_multiset_X_sub_C_mul Polynomial.exists_prod_multiset_x_sub_c_mul
-
+#align polynomial.exists_prod_multiset_X_sub_C_mul Polynomial.exists_prod_multiset_X_sub_C_mul
+
+/- warning: polynomial.C_leading_coeff_mul_prod_multiset_X_sub_C -> Polynomial.c_leadingCoeff_mul_prod_multiset_X_sub_C 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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Eq.{1} Nat (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) 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+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))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) (fun (_x : Multiset.{u1} R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} R) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} R) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} 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_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))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) (Multiset.prod.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) (CommRing.toCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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 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(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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)))) p)
+Case conversion may be inaccurate. Consider using '#align polynomial.C_leading_coeff_mul_prod_multiset_X_sub_C Polynomial.c_leadingCoeff_mul_prod_multiset_X_sub_Cₓ'. -/
 /-- A polynomial `p` that has as many roots as its degree
 can be written `p = p.leading_coeff * ∏(X - a)`, for `a` in `p.roots`. -/
-theorem c_leadingCoeff_mul_prod_multiset_x_sub_c (hroots : p.roots.card = p.natDegree) :
+theorem c_leadingCoeff_mul_prod_multiset_X_sub_C (hroots : p.roots.card = p.natDegree) :
     C p.leadingCoeff * (p.roots.map fun a => X - C a).Prod = p :=
-  (eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le monic_prod_multiset_x_sub_c
-      p.prod_multiset_x_sub_c_dvd
-      ((natDegree_multiset_prod_x_sub_c_eq_card _).trans hroots).ge).symm
-#align polynomial.C_leading_coeff_mul_prod_multiset_X_sub_C Polynomial.c_leadingCoeff_mul_prod_multiset_x_sub_c
-
+  (eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le monic_prod_multiset_X_sub_C
+      p.prod_multiset_X_sub_C_dvd
+      ((natDegree_multiset_prod_X_sub_C_eq_card _).trans hroots).ge).symm
+#align polynomial.C_leading_coeff_mul_prod_multiset_X_sub_C Polynomial.c_leadingCoeff_mul_prod_multiset_X_sub_C
+
+/- warning: polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq -> Polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq 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))] {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.{1} Nat (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} R) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} R) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} R) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} R) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} R) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} R) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} R) (Multiset.orderedCancelAddCommMonoid.{u1} R)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} R) (Polynomial.roots.{u1} R _inst_1 _inst_2 p)) (Polynomial.natDegree.{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))) (Multiset.prod.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, 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))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (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))) a)) (Polynomial.roots.{u1} R _inst_1 _inst_2 p))) p)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq Polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eqₓ'. -/
 /-- A monic polynomial `p` that has as many roots as its degree
 can be written `p = ∏(X - a)`, for `a` in `p.roots`. -/
-theorem prod_multiset_x_sub_c_of_monic_of_roots_card_eq (hp : p.Monic)
+theorem prod_multiset_X_sub_C_of_monic_of_roots_card_eq (hp : p.Monic)
     (hroots : p.roots.card = p.natDegree) : (p.roots.map fun a => X - C a).Prod = p :=
   by
   convert C_leading_coeff_mul_prod_multiset_X_sub_C hroots
   rw [hp.leading_coeff, C_1, one_mul]
-#align polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq Polynomial.prod_multiset_x_sub_c_of_monic_of_roots_card_eq
+#align polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq Polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq
 
 end CommRing
 
@@ -1129,6 +1741,12 @@ section
 
 variable {A B : Type _} [CommRing A] [CommRing B]
 
+/- warning: polynomial.le_root_multiplicity_map -> Polynomial.le_rootMultiplicity_map is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommRing.{u1} A] [_inst_2 : CommRing.{u2} B] {p : Polynomial.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))} {f : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))}, (Ne.{succ u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p) (OfNat.ofNat.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) 0 (OfNat.mk.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) 0 (Zero.zero.{u2} (Polynomial.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))) (Polynomial.zero.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2))))))) -> (forall (a : A), LE.le.{0} Nat Nat.hasLe (Polynomial.rootMultiplicity.{u1} A _inst_1 a p) (Polynomial.rootMultiplicity.{u2} B _inst_2 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) (fun (_x : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) => A -> B) (RingHom.hasCoeToFun.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) f a) (Polynomial.map.{u1, u2} A B (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) f p)))
+but is expected to have type
+  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] {p : Polynomial.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))} {f : RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))}, (Ne.{succ u1} (Polynomial.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2))) (Polynomial.map.{u2, u1} A B (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1)) (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2)) f p) (OfNat.ofNat.{u1} (Polynomial.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2))) (Polynomial.zero.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2)))))) -> (forall (a : A), LE.le.{0} Nat instLENat (Polynomial.rootMultiplicity.{u2} A _inst_1 a p) (Polynomial.rootMultiplicity.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) _inst_2 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))))) f a) (Polynomial.map.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1)) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) _inst_2)) f p)))
+Case conversion may be inaccurate. Consider using '#align polynomial.le_root_multiplicity_map Polynomial.le_rootMultiplicity_mapₓ'. -/
 theorem le_rootMultiplicity_map {p : A[X]} {f : A →+* B} (hmap : map f p ≠ 0) (a : A) :
     rootMultiplicity a p ≤ rootMultiplicity (f a) (p.map f) :=
   by
@@ -1137,6 +1755,12 @@ theorem le_rootMultiplicity_map {p : A[X]} {f : A →+* B} (hmap : map f p ≠ 0
   rw [map_pow, map_sub, coe_map_ring_hom, map_X, map_C]
 #align polynomial.le_root_multiplicity_map Polynomial.le_rootMultiplicity_map
 
+/- warning: polynomial.eq_root_multiplicity_map -> Polynomial.eq_rootMultiplicity_map is a dubious translation:
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+but is expected to have type
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))))) f a) (Polynomial.map.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1)) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) a) _inst_2)) f p)))
+Case conversion may be inaccurate. Consider using '#align polynomial.eq_root_multiplicity_map Polynomial.eq_rootMultiplicity_mapₓ'. -/
 theorem eq_rootMultiplicity_map {p : A[X]} {f : A →+* B} (hf : Function.Injective f) (a : A) :
     rootMultiplicity a p = rootMultiplicity (f a) (p.map f) :=
   by
@@ -1147,6 +1771,12 @@ theorem eq_rootMultiplicity_map {p : A[X]} {f : A →+* B} (hf : Function.Inject
   apply pow_root_multiplicity_dvd
 #align polynomial.eq_root_multiplicity_map Polynomial.eq_rootMultiplicity_map
 
+/- warning: polynomial.count_map_roots -> Polynomial.count_map_roots 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.count_map_roots Polynomial.count_map_rootsₓ'. -/
 theorem count_map_roots [IsDomain A] {p : A[X]} {f : A →+* B} (hmap : map f p ≠ 0) (b : B) :
     (p.roots.map f).count b ≤ rootMultiplicity b (p.map f) :=
   by
@@ -1160,6 +1790,12 @@ theorem count_map_roots [IsDomain A] {p : A[X]} {f : A →+* B} (hmap : map f p
   simp only [Function.comp_apply, Polynomial.map_sub, map_X, map_C]
 #align polynomial.count_map_roots Polynomial.count_map_roots
 
+/- warning: polynomial.count_map_roots_of_injective -> Polynomial.count_map_roots_of_injective is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.count_map_roots_of_injective Polynomial.count_map_roots_of_injectiveₓ'. -/
 theorem count_map_roots_of_injective [IsDomain A] (p : A[X]) {f : A →+* B}
     (hf : Function.Injective f) (b : B) : (p.roots.map f).count b ≤ rootMultiplicity b (p.map f) :=
   by
@@ -1170,6 +1806,12 @@ theorem count_map_roots_of_injective [IsDomain A] (p : A[X]) {f : A →+* B}
   · exact count_map_roots ((Polynomial.map_ne_zero_iff hf).mpr hp0) b
 #align polynomial.count_map_roots_of_injective Polynomial.count_map_roots_of_injective
 
+/- warning: polynomial.map_roots_le -> Polynomial.map_roots_le 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.map_roots_le Polynomial.map_roots_leₓ'. -/
 theorem map_roots_le [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (h : p.map f ≠ 0) :
     p.roots.map f ≤ (p.map f).roots :=
   Multiset.le_iff_count.2 fun b => by
@@ -1177,6 +1819,12 @@ theorem map_roots_le [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (h : p
     apply count_map_roots h
 #align polynomial.map_roots_le Polynomial.map_roots_le
 
+/- warning: polynomial.map_roots_le_of_injective -> Polynomial.map_roots_le_of_injective is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.map_roots_le_of_injective Polynomial.map_roots_le_of_injectiveₓ'. -/
 theorem map_roots_le_of_injective [IsDomain A] [IsDomain B] (p : A[X]) {f : A →+* B}
     (hf : Function.Injective f) : p.roots.map f ≤ (p.map f).roots :=
   by
@@ -1184,6 +1832,12 @@ theorem map_roots_le_of_injective [IsDomain A] [IsDomain B] (p : A[X]) {f : A 
   exact map_roots_le ((Polynomial.map_ne_zero_iff hf).mpr hp0)
 #align polynomial.map_roots_le_of_injective Polynomial.map_roots_le_of_injective
 
+/- warning: polynomial.card_roots_le_map -> Polynomial.card_roots_le_map 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.card_roots_le_map Polynomial.card_roots_le_mapₓ'. -/
 theorem card_roots_le_map [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (h : p.map f ≠ 0) :
     p.roots.card ≤ (p.map f).roots.card :=
   by
@@ -1191,6 +1845,12 @@ theorem card_roots_le_map [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (
   exact Multiset.card_le_of_le (map_roots_le h)
 #align polynomial.card_roots_le_map Polynomial.card_roots_le_map
 
+/- warning: polynomial.card_roots_le_map_of_injective -> Polynomial.card_roots_le_map_of_injective is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_3 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))] [_inst_4 : IsDomain.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2))] {p : Polynomial.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))} {f : RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))))) f)) -> (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} A) => Nat) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) instLENat (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} A) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} A) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} A) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} A) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} A)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} A) (fun (_x : Multiset.{u2} A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} A) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} A) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} A) 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(AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} B) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} B) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} B) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} B) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} B) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} B) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} B) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} B) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} B)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} B) (Polynomial.roots.{u1} B _inst_2 _inst_4 (Polynomial.map.{u2, u1} A B (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1)) (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2)) f p))))
+Case conversion may be inaccurate. Consider using '#align polynomial.card_roots_le_map_of_injective Polynomial.card_roots_le_map_of_injectiveₓ'. -/
 theorem card_roots_le_map_of_injective [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B}
     (hf : Function.Injective f) : p.roots.card ≤ (p.map f).roots.card :=
   by
@@ -1198,6 +1858,12 @@ theorem card_roots_le_map_of_injective [IsDomain A] [IsDomain B] {p : A[X]} {f :
   exact card_roots_le_map ((Polynomial.map_ne_zero_iff hf).mpr hp0)
 #align polynomial.card_roots_le_map_of_injective Polynomial.card_roots_le_map_of_injective
 
+/- warning: polynomial.roots_map_of_injective_of_card_eq_nat_degree -> Polynomial.roots_map_of_injective_of_card_eq_natDegree is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2)))) A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_2))))))) f) (Polynomial.roots.{u2} A _inst_1 _inst_3 p)) (Polynomial.roots.{u1} B _inst_2 _inst_4 (Polynomial.map.{u2, u1} A B (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1)) (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_2)) f p)))
+Case conversion may be inaccurate. Consider using '#align polynomial.roots_map_of_injective_of_card_eq_nat_degree Polynomial.roots_map_of_injective_of_card_eq_natDegreeₓ'. -/
 theorem roots_map_of_injective_of_card_eq_natDegree [IsDomain A] [IsDomain B] {p : A[X]}
     {f : A →+* B} (hf : Function.Injective f) (hroots : p.roots.card = p.natDegree) :
     p.roots.map f = (p.map f).roots :=
@@ -1212,6 +1878,12 @@ section
 
 variable [Semiring R] [CommRing S] [IsDomain S] (φ : R →+* S)
 
+/- warning: polynomial.is_unit_of_is_unit_leading_coeff_of_is_unit_map -> Polynomial.isUnit_of_isUnit_leadingCoeff_of_isUnit_map is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (φ : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) {f : Polynomial.{u1} R _inst_1}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) -> (IsUnit.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ring.toMonoid.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Polynomial.ring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Polynomial.map.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) φ f)) -> (IsUnit.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) f)
+but is expected to have type
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : CommRing.{u2} S] [_inst_3 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (φ : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) {f : Polynomial.{u1} R _inst_1}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) -> (IsUnit.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (MonoidWithZero.toMonoid.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Semiring.toMonoidWithZero.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Polynomial.semiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Polynomial.map.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) φ f)) -> (IsUnit.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) f)
+Case conversion may be inaccurate. Consider using '#align polynomial.is_unit_of_is_unit_leading_coeff_of_is_unit_map Polynomial.isUnit_of_isUnit_leadingCoeff_of_isUnit_mapₓ'. -/
 theorem isUnit_of_isUnit_leadingCoeff_of_isUnit_map {f : R[X]} (hf : IsUnit f.leadingCoeff)
     (H : IsUnit (map φ f)) : IsUnit f :=
   by
@@ -1235,6 +1907,12 @@ section
 
 variable [CommRing R] [IsDomain R] [CommRing S] [IsDomain S] (φ : R →+* S)
 
+/- warning: polynomial.monic.irreducible_of_irreducible_map -> Polynomial.Monic.irreducible_of_irreducible_map is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : CommRing.{u2} S] [_inst_4 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3))] (φ : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_3)))) (f : 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)) f) -> (Irreducible.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3))) (Ring.toMonoid.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3))) (Polynomial.ring.{u2} S (CommRing.toRing.{u2} S _inst_3))) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3)) φ f)) -> (Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)
+but is expected to have type
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : CommRing.{u2} S] [_inst_4 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3))] (φ : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_3)))) (f : 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)) f) -> (Irreducible.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3))) (MonoidWithZero.toMonoid.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3))) (Semiring.toMonoidWithZero.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3))) (Polynomial.semiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3))))) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3)) φ f)) -> (Irreducible.{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))) (Semiring.toMonoidWithZero.{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))))) f)
+Case conversion may be inaccurate. Consider using '#align polynomial.monic.irreducible_of_irreducible_map Polynomial.Monic.irreducible_of_irreducible_mapₓ'. -/
 /-- A polynomial over an integral domain `R` is irreducible if it is monic and
   irreducible after mapping into an integral domain `S`.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/2af0836443b4cfb5feda0df0051acdb398304931

@@ -406,7 +406,7 @@ section Roots
 open Multiset
 
 theorem prime_x_sub_c (r : R) : Prime (X - C r) :=
-  ⟨X_sub_C_ne_zero r, not_isUnit_x_sub_c r, fun _ _ =>
+  ⟨X_sub_C_ne_zero r, not_isUnit_X_sub_C r, fun _ _ =>
     by
     simp_rw [dvd_iff_is_root, is_root.def, eval_mul, mul_eq_zero]
     exact id⟩

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

@@ -116,7 +116,8 @@ variable [Ring S]
 theorem aeval_modByMonic_eq_self_of_root [Algebra R S] {p q : R[X]} (hq : q.Monic) {x : S}
     (hx : aeval x q = 0) : aeval x (p %ₘ q) = aeval x p :=
   by-- `eval₂_mod_by_monic_eq_self_of_root` doesn't work here as it needs commutativity
-  rw [mod_by_monic_eq_sub_mul_div p hq, _root_.map_sub, _root_.map_mul, hx, zero_mul, sub_zero]
+  rw [mod_by_monic_eq_sub_mul_div p hq, _root_.map_sub, _root_.map_mul, hx, MulZeroClass.zero_mul,
+    sub_zero]
 #align polynomial.aeval_mod_by_monic_eq_self_of_root Polynomial.aeval_modByMonic_eq_self_of_root
 
 end
@@ -143,9 +144,9 @@ theorem natDegree_mul (hp : p ≠ 0) (hq : q ≠ 0) : natDegree (p * q) = natDeg
 theorem trailingDegree_mul : (p * q).trailingDegree = p.trailingDegree + q.trailingDegree :=
   by
   by_cases hp : p = 0
-  · rw [hp, zero_mul, trailing_degree_zero, top_add]
+  · rw [hp, MulZeroClass.zero_mul, trailing_degree_zero, top_add]
   by_cases hq : q = 0
-  · rw [hq, mul_zero, trailing_degree_zero, add_top]
+  · rw [hq, MulZeroClass.mul_zero, trailing_degree_zero, add_top]
   rw [trailing_degree_eq_nat_trailing_degree hp, trailing_degree_eq_nat_trailing_degree hq,
     trailing_degree_eq_nat_trailing_degree (mul_ne_zero hp hq), nat_trailing_degree_mul hp hq,
     WithTop.coe_add]
@@ -162,7 +163,7 @@ theorem natDegree_pow (p : R[X]) (n : ℕ) : natDegree (p ^ n) = n * natDegree p
 #align polynomial.nat_degree_pow Polynomial.natDegree_pow
 
 theorem degree_le_mul_left (p : R[X]) (hq : q ≠ 0) : degree p ≤ degree (p * q) :=
-  if hp : p = 0 then by simp only [hp, zero_mul, le_refl]
+  if hp : p = 0 then by simp only [hp, MulZeroClass.zero_mul, le_refl]
   else by
     rw [degree_mul, degree_eq_nat_degree hp, degree_eq_nat_degree hq] <;>
       exact WithBot.coe_le_coe.2 (Nat.le_add_right _ _)
@@ -488,7 +489,7 @@ theorem exists_multiset_roots :
       let ⟨x, hx⟩ := h
       have hpd : 0 < degree p := degree_pos_of_root hp hx
       have hd0 : p /ₘ (X - C x) ≠ 0 := fun h => by
-        rw [← mul_div_by_monic_eq_iff_is_root.2 hx, h, mul_zero] at hp <;> exact hp rfl
+        rw [← mul_div_by_monic_eq_iff_is_root.2 hx, h, MulZeroClass.mul_zero] at hp <;> exact hp rfl
       have wf : degree (p /ₘ _) < degree p :=
         degree_div_by_monic_lt _ (monic_X_sub_C x) hp ((degree_X_sub_C x).symm ▸ by decide)
       let ⟨t, htd, htr⟩ := @exists_multiset_roots (p /ₘ (X - C x)) hd0
@@ -664,7 +665,7 @@ theorem roots_one : (1 : R[X]).roots = ∅ :=
 theorem roots_c_mul (p : R[X]) (ha : a ≠ 0) : (C a * p).roots = p.roots := by
   by_cases hp : p = 0 <;>
     simp only [roots_mul, *, Ne.def, mul_eq_zero, C_eq_zero, or_self_iff, not_false_iff, roots_C,
-      zero_add, mul_zero]
+      zero_add, MulZeroClass.mul_zero]
 #align polynomial.roots_C_mul Polynomial.roots_c_mul
 
 @[simp]
@@ -1093,7 +1094,7 @@ theorem exists_prod_multiset_x_sub_c_mul (p : R[X]) :
   obtain ⟨q, he⟩ := p.prod_multiset_X_sub_C_dvd
   use q, he.symm
   obtain rfl | hq := eq_or_ne q 0
-  · rw [mul_zero] at he
+  · rw [MulZeroClass.mul_zero] at he
     subst he
     simp
   constructor

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

@@ -1052,7 +1052,7 @@ theorem pairwise_coprime_x_sub_c {K} [Field K] {I : Type v} {s : I → K} (H : F
 #align polynomial.pairwise_coprime_X_sub_C Polynomial.pairwise_coprime_x_sub_c
 
 theorem monic_prod_multiset_x_sub_c : Monic (p.roots.map fun a => X - C a).Prod :=
-  monic_multiset_prod_of_monic _ _ fun a _ => monic_x_sub_c a
+  monic_multiset_prod_of_monic _ _ fun a _ => monic_X_sub_C a
 #align polynomial.monic_prod_multiset_X_sub_C Polynomial.monic_prod_multiset_x_sub_c
 
 theorem prod_multiset_root_eq_finset_root :

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

@@ -236,7 +236,7 @@ theorem degree_coe_units [Nontrivial R] (u : R[X]ˣ) : degree (u : R[X]) = 0 :=
 theorem isUnit_iff : IsUnit p ↔ ∃ r : R, IsUnit r ∧ C r = p :=
   ⟨fun hp =>
     ⟨p.coeff 0,
-      let h := eq_c_of_natDegree_eq_zero (natDegree_eq_zero_of_isUnit hp)
+      let h := eq_C_of_natDegree_eq_zero (natDegree_eq_zero_of_isUnit hp)
       ⟨isUnit_C.1 (h ▸ hp), h.symm⟩⟩,
     fun ⟨r, hr, hrp⟩ => hrp ▸ isUnit_C.2 hr⟩
 #align polynomial.is_unit_iff Polynomial.isUnit_iff
@@ -246,7 +246,7 @@ variable [CharZero R]
 @[simp]
 theorem degree_bit0_eq (p : R[X]) : degree (bit0 p) = degree p := by
   rw [bit0_eq_two_mul, degree_mul, (by simp : (2 : R[X]) = C 2),
-    @Polynomial.degree_c R _ _ two_ne_zero, zero_add]
+    @Polynomial.degree_C R _ _ two_ne_zero, zero_add]
 #align polynomial.degree_bit0_eq Polynomial.degree_bit0_eq
 
 @[simp]
@@ -405,7 +405,7 @@ section Roots
 open Multiset
 
 theorem prime_x_sub_c (r : R) : Prime (X - C r) :=
-  ⟨x_sub_c_ne_zero r, not_isUnit_x_sub_c r, fun _ _ =>
+  ⟨X_sub_C_ne_zero r, not_isUnit_x_sub_c r, fun _ _ =>
     by
     simp_rw [dvd_iff_is_root, is_root.def, eval_mul, mul_eq_zero]
     exact id⟩
@@ -550,7 +550,7 @@ theorem card_roots_sub_c {p : R[X]} {a : R} (hp0 : 0 < degree p) :
     ((p - C a).roots.card : WithBot ℕ) ≤ degree p :=
   calc
     ((p - C a).roots.card : WithBot ℕ) ≤ degree (p - C a) :=
-      card_roots <| mt sub_eq_zero.1 fun h => not_le_of_gt hp0 <| h.symm ▸ degree_c_le
+      card_roots <| mt sub_eq_zero.1 fun h => not_le_of_gt hp0 <| h.symm ▸ degree_C_le
     _ = degree p := by rw [sub_eq_add_neg, ← C_neg] <;> exact degree_add_C hp0
     
 #align polynomial.card_roots_sub_C Polynomial.card_roots_sub_c
@@ -633,7 +633,7 @@ theorem mem_roots_sub_C' {p : R[X]} {a x : R} : x ∈ (p - C a).roots ↔ p ≠
 
 theorem mem_roots_sub_c {p : R[X]} {a x : R} (hp0 : 0 < degree p) :
     x ∈ (p - C a).roots ↔ p.eval x = a :=
-  mem_roots_sub_C'.trans <| and_iff_right fun hp => hp0.not_le <| hp.symm ▸ degree_c_le
+  mem_roots_sub_C'.trans <| and_iff_right fun hp => hp0.not_le <| hp.symm ▸ degree_C_le
 #align polynomial.mem_roots_sub_C Polynomial.mem_roots_sub_c
 
 @[simp]
@@ -719,7 +719,7 @@ theorem roots_monomial (ha : a ≠ 0) (n : ℕ) : (monomial n a).roots = n • {
 #align polynomial.roots_monomial Polynomial.roots_monomial
 
 theorem roots_prod_x_sub_c (s : Finset R) : (s.Prod fun a => X - C a).roots = s.val :=
-  (roots_prod (fun a => X - C a) s (prod_ne_zero_iff.mpr fun a _ => x_sub_c_ne_zero a)).trans
+  (roots_prod (fun a => X - C a) s (prod_ne_zero_iff.mpr fun a _ => X_sub_C_ne_zero a)).trans
     (by simp_rw [roots_X_sub_C, Multiset.bind_singleton, Multiset.map_id'])
 #align polynomial.roots_prod_X_sub_C Polynomial.roots_prod_x_sub_c
 
@@ -749,8 +749,8 @@ theorem card_roots_x_pow_sub_c {n : ℕ} (hn : 0 < n) (a : R) :
   WithBot.coe_le_coe.1 <|
     calc
       ((roots ((X : R[X]) ^ n - C a)).card : WithBot ℕ) ≤ degree ((X : R[X]) ^ n - C a) :=
-        card_roots (x_pow_sub_c_ne_zero hn a)
-      _ = n := degree_x_pow_sub_c hn a
+        card_roots (X_pow_sub_C_ne_zero hn a)
+      _ = n := degree_X_pow_sub_C hn a
       
 #align polynomial.card_roots_X_pow_sub_C Polynomial.card_roots_x_pow_sub_c
 
@@ -825,7 +825,7 @@ theorem Monic.comp_x_sub_c (hp : p.Monic) (r : R) : (p.comp (X - C r)).Monic :=
 #align polynomial.monic.comp_X_sub_C Polynomial.Monic.comp_x_sub_c
 
 theorem units_coeff_zero_smul (c : R[X]ˣ) (p : R[X]) : (c : R[X]).coeff 0 • p = c * p := by
-  rw [← Polynomial.C_mul', ← Polynomial.eq_c_of_degree_eq_zero (degree_coe_units c)]
+  rw [← Polynomial.C_mul', ← Polynomial.eq_C_of_degree_eq_zero (degree_coe_units c)]
 #align polynomial.units_coeff_zero_smul Polynomial.units_coeff_zero_smul
 
 @[simp]
@@ -984,7 +984,7 @@ theorem degree_eq_one_of_irreducible_of_root (hi : Irreducible p) {x : R} (hx :
   have : IsUnit (X - C x) ∨ IsUnit g := hi.isUnit_or_isUnit hg
   this.elim
     (fun h => by
-      have h₁ : degree (X - C x) = 1 := degree_x_sub_c x
+      have h₁ : degree (X - C x) = 1 := degree_X_sub_C x
       have h₂ : degree (X - C x) = 0 := degree_eq_zero_of_isUnit h
       rw [h₁] at h₂ <;> exact absurd h₂ (by decide))
     fun hgu => by rw [hg, degree_mul, degree_X_sub_C, degree_eq_zero_of_is_unit hgu, add_zero]

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

@@ -233,12 +233,12 @@ theorem degree_coe_units [Nontrivial R] (u : R[X]ˣ) : degree (u : R[X]) = 0 :=
   degree_eq_zero_of_isUnit ⟨u, rfl⟩
 #align polynomial.degree_coe_units Polynomial.degree_coe_units
 
-theorem isUnit_iff : IsUnit p ↔ ∃ r : R, IsUnit r ∧ c r = p :=
+theorem isUnit_iff : IsUnit p ↔ ∃ r : R, IsUnit r ∧ C r = p :=
   ⟨fun hp =>
     ⟨p.coeff 0,
       let h := eq_c_of_natDegree_eq_zero (natDegree_eq_zero_of_isUnit hp)
-      ⟨isUnit_c.1 (h ▸ hp), h.symm⟩⟩,
-    fun ⟨r, hr, hrp⟩ => hrp ▸ isUnit_c.2 hr⟩
+      ⟨isUnit_C.1 (h ▸ hp), h.symm⟩⟩,
+    fun ⟨r, hr, hrp⟩ => hrp ▸ isUnit_C.2 hr⟩
 #align polynomial.is_unit_iff Polynomial.isUnit_iff
 
 variable [CharZero R]
@@ -370,7 +370,7 @@ variable [CommRing R]
 /-- The multiplicity of `a` as root of a nonzero polynomial `p` is at least `n` iff
   `(X - a) ^ n` divides `p`. -/
 theorem le_rootMultiplicity_iff {p : R[X]} (p0 : p ≠ 0) {a : R} {n : ℕ} :
-    n ≤ rootMultiplicity a p ↔ (x - c a) ^ n ∣ p :=
+    n ≤ rootMultiplicity a p ↔ (X - C a) ^ n ∣ p :=
   by
   simp_rw [root_multiplicity, dif_neg p0, Nat.le_find_iff, Classical.not_not]
   refine' ⟨fun h => _, fun h m hm => (pow_dvd_pow _ hm).trans h⟩
@@ -380,12 +380,12 @@ theorem le_rootMultiplicity_iff {p : R[X]} (p0 : p ≠ 0) {a : R} {n : ℕ} :
 #align polynomial.le_root_multiplicity_iff Polynomial.le_rootMultiplicity_iff
 
 theorem rootMultiplicity_le_iff {p : R[X]} (p0 : p ≠ 0) (a : R) (n : ℕ) :
-    rootMultiplicity a p ≤ n ↔ ¬(x - c a) ^ (n + 1) ∣ p := by
+    rootMultiplicity a p ≤ n ↔ ¬(X - C a) ^ (n + 1) ∣ p := by
   rw [← (le_root_multiplicity_iff p0).Not, not_le, Nat.lt_add_one_iff]
 #align polynomial.root_multiplicity_le_iff Polynomial.rootMultiplicity_le_iff
 
 theorem pow_rootMultiplicity_not_dvd {p : R[X]} (p0 : p ≠ 0) (a : R) :
-    ¬(x - c a) ^ (rootMultiplicity a p + 1) ∣ p := by rw [← root_multiplicity_le_iff p0]
+    ¬(X - C a) ^ (rootMultiplicity a p + 1) ∣ p := by rw [← root_multiplicity_le_iff p0]
 #align polynomial.pow_root_multiplicity_not_dvd Polynomial.pow_rootMultiplicity_not_dvd
 
 /-- The multiplicity of `p + q` is at least the minimum of the multiplicities. -/
@@ -404,29 +404,29 @@ section Roots
 
 open Multiset
 
-theorem prime_x_sub_c (r : R) : Prime (x - c r) :=
+theorem prime_x_sub_c (r : R) : Prime (X - C r) :=
   ⟨x_sub_c_ne_zero r, not_isUnit_x_sub_c r, fun _ _ =>
     by
     simp_rw [dvd_iff_is_root, is_root.def, eval_mul, mul_eq_zero]
     exact id⟩
 #align polynomial.prime_X_sub_C Polynomial.prime_x_sub_c
 
-theorem prime_x : Prime (x : R[X]) :=
+theorem prime_x : Prime (X : R[X]) :=
   by
   convert prime_X_sub_C (0 : R)
   simp
 #align polynomial.prime_X Polynomial.prime_x
 
 theorem Monic.prime_of_degree_eq_one (hp1 : degree p = 1) (hm : Monic p) : Prime p :=
-  have : p = x - c (-p.coeff 0) := by simpa [hm.leading_coeff] using eq_X_add_C_of_degree_eq_one hp1
+  have : p = X - C (-p.coeff 0) := by simpa [hm.leading_coeff] using eq_X_add_C_of_degree_eq_one hp1
   this.symm ▸ prime_x_sub_c _
 #align polynomial.monic.prime_of_degree_eq_one Polynomial.Monic.prime_of_degree_eq_one
 
-theorem irreducible_x_sub_c (r : R) : Irreducible (x - c r) :=
+theorem irreducible_x_sub_c (r : R) : Irreducible (X - C r) :=
   (prime_x_sub_c r).Irreducible
 #align polynomial.irreducible_X_sub_C Polynomial.irreducible_x_sub_c
 
-theorem irreducible_x : Irreducible (x : R[X]) :=
+theorem irreducible_x : Irreducible (X : R[X]) :=
   Prime.irreducible prime_x
 #align polynomial.irreducible_X Polynomial.irreducible_x
 
@@ -454,13 +454,13 @@ theorem rootMultiplicity_mul {p q : R[X]} {x : R} (hpq : p * q ≠ 0) :
     multiplicity.mul' (prime_X_sub_C x)]
 #align polynomial.root_multiplicity_mul Polynomial.rootMultiplicity_mul
 
-theorem rootMultiplicity_x_sub_c_self {x : R} : rootMultiplicity x (x - c x) = 1 := by
+theorem rootMultiplicity_x_sub_c_self {x : R} : rootMultiplicity x (X - C x) = 1 := by
   rw [root_multiplicity_eq_multiplicity, dif_neg (X_sub_C_ne_zero x),
     multiplicity.get_multiplicity_self]
 #align polynomial.root_multiplicity_X_sub_C_self Polynomial.rootMultiplicity_x_sub_c_self
 
 theorem rootMultiplicity_x_sub_c {x y : R} :
-    rootMultiplicity x (x - c y) = if x = y then 1 else 0 :=
+    rootMultiplicity x (X - C y) = if x = y then 1 else 0 :=
   by
   split_ifs with hxy
   · rw [hxy]
@@ -469,7 +469,7 @@ theorem rootMultiplicity_x_sub_c {x y : R} :
 #align polynomial.root_multiplicity_X_sub_C Polynomial.rootMultiplicity_x_sub_c
 
 /-- The multiplicity of `a` as root of `(X - a) ^ n` is `n`. -/
-theorem rootMultiplicity_x_sub_c_pow (a : R) (n : ℕ) : rootMultiplicity a ((x - c a) ^ n) = n :=
+theorem rootMultiplicity_x_sub_c_pow (a : R) (n : ℕ) : rootMultiplicity a ((X - C a) ^ n) = n :=
   by
   induction' n with n hn
   · refine' root_multiplicity_eq_zero _
@@ -547,16 +547,16 @@ theorem card_roots' (p : R[X]) : p.roots.card ≤ natDegree p :=
 #align polynomial.card_roots' Polynomial.card_roots'
 
 theorem card_roots_sub_c {p : R[X]} {a : R} (hp0 : 0 < degree p) :
-    ((p - c a).roots.card : WithBot ℕ) ≤ degree p :=
+    ((p - C a).roots.card : WithBot ℕ) ≤ degree p :=
   calc
-    ((p - c a).roots.card : WithBot ℕ) ≤ degree (p - c a) :=
+    ((p - C a).roots.card : WithBot ℕ) ≤ degree (p - C a) :=
       card_roots <| mt sub_eq_zero.1 fun h => not_le_of_gt hp0 <| h.symm ▸ degree_c_le
     _ = degree p := by rw [sub_eq_add_neg, ← C_neg] <;> exact degree_add_C hp0
     
 #align polynomial.card_roots_sub_C Polynomial.card_roots_sub_c
 
 theorem card_roots_sub_C' {p : R[X]} {a : R} (hp0 : 0 < degree p) :
-    (p - c a).roots.card ≤ natDegree p :=
+    (p - C a).roots.card ≤ natDegree p :=
   WithBot.coe_le_coe.1
     (le_trans (card_roots_sub_c hp0)
       (le_of_eq <| degree_eq_natDegree fun h => by simp_all [lt_irrefl]))
@@ -627,28 +627,28 @@ theorem roots.le_of_dvd (h : q ≠ 0) : p ∣ q → roots p ≤ roots q :=
   exact multiset.le_iff_exists_add.mpr ⟨k.roots, roots_mul h⟩
 #align polynomial.roots.le_of_dvd Polynomial.roots.le_of_dvd
 
-theorem mem_roots_sub_C' {p : R[X]} {a x : R} : x ∈ (p - c a).roots ↔ p ≠ c a ∧ p.eval x = a := by
+theorem mem_roots_sub_C' {p : R[X]} {a x : R} : x ∈ (p - C a).roots ↔ p ≠ C a ∧ p.eval x = a := by
   rw [mem_roots', is_root.def, sub_ne_zero, eval_sub, sub_eq_zero, eval_C]
 #align polynomial.mem_roots_sub_C' Polynomial.mem_roots_sub_C'
 
 theorem mem_roots_sub_c {p : R[X]} {a x : R} (hp0 : 0 < degree p) :
-    x ∈ (p - c a).roots ↔ p.eval x = a :=
+    x ∈ (p - C a).roots ↔ p.eval x = a :=
   mem_roots_sub_C'.trans <| and_iff_right fun hp => hp0.not_le <| hp.symm ▸ degree_c_le
 #align polynomial.mem_roots_sub_C Polynomial.mem_roots_sub_c
 
 @[simp]
-theorem roots_x_sub_c (r : R) : roots (x - c r) = {r} :=
+theorem roots_x_sub_c (r : R) : roots (X - C r) = {r} :=
   by
   ext s
   rw [count_roots, root_multiplicity_X_sub_C, count_singleton]
 #align polynomial.roots_X_sub_C Polynomial.roots_x_sub_c
 
 @[simp]
-theorem roots_x : roots (x : R[X]) = {0} := by rw [← roots_X_sub_C, C_0, sub_zero]
+theorem roots_x : roots (X : R[X]) = {0} := by rw [← roots_X_sub_C, C_0, sub_zero]
 #align polynomial.roots_X Polynomial.roots_x
 
 @[simp]
-theorem roots_c (x : R) : (c x).roots = 0 :=
+theorem roots_c (x : R) : (C x).roots = 0 :=
   if H : x = 0 then by rw [H, C_0, roots_zero]
   else
     Multiset.ext.mpr fun r => by
@@ -661,7 +661,7 @@ theorem roots_one : (1 : R[X]).roots = ∅ :=
 #align polynomial.roots_one Polynomial.roots_one
 
 @[simp]
-theorem roots_c_mul (p : R[X]) (ha : a ≠ 0) : (c a * p).roots = p.roots := by
+theorem roots_c_mul (p : R[X]) (ha : a ≠ 0) : (C a * p).roots = p.roots := by
   by_cases hp : p = 0 <;>
     simp only [roots_mul, *, Ne.def, mul_eq_zero, C_eq_zero, or_self_iff, not_false_iff, roots_C,
       zero_add, mul_zero]
@@ -706,10 +706,10 @@ theorem roots_pow (p : R[X]) (n : ℕ) : (p ^ n).roots = n • p.roots :=
         add_smul, one_smul]
 #align polynomial.roots_pow Polynomial.roots_pow
 
-theorem roots_x_pow (n : ℕ) : (x ^ n : R[X]).roots = n • {0} := by rw [roots_pow, roots_X]
+theorem roots_x_pow (n : ℕ) : (X ^ n : R[X]).roots = n • {0} := by rw [roots_pow, roots_X]
 #align polynomial.roots_X_pow Polynomial.roots_x_pow
 
-theorem roots_c_mul_x_pow (ha : a ≠ 0) (n : ℕ) : (c a * x ^ n).roots = n • {0} := by
+theorem roots_c_mul_x_pow (ha : a ≠ 0) (n : ℕ) : (C a * X ^ n).roots = n • {0} := by
   rw [roots_C_mul _ ha, roots_X_pow]
 #align polynomial.roots_C_mul_X_pow Polynomial.roots_c_mul_x_pow
 
@@ -718,13 +718,13 @@ theorem roots_monomial (ha : a ≠ 0) (n : ℕ) : (monomial n a).roots = n • {
   rw [← C_mul_X_pow_eq_monomial, roots_C_mul_X_pow ha]
 #align polynomial.roots_monomial Polynomial.roots_monomial
 
-theorem roots_prod_x_sub_c (s : Finset R) : (s.Prod fun a => x - c a).roots = s.val :=
-  (roots_prod (fun a => x - c a) s (prod_ne_zero_iff.mpr fun a _ => x_sub_c_ne_zero a)).trans
+theorem roots_prod_x_sub_c (s : Finset R) : (s.Prod fun a => X - C a).roots = s.val :=
+  (roots_prod (fun a => X - C a) s (prod_ne_zero_iff.mpr fun a _ => x_sub_c_ne_zero a)).trans
     (by simp_rw [roots_X_sub_C, Multiset.bind_singleton, Multiset.map_id'])
 #align polynomial.roots_prod_X_sub_C Polynomial.roots_prod_x_sub_c
 
 @[simp]
-theorem roots_multiset_prod_x_sub_c (s : Multiset R) : (s.map fun a => x - c a).Prod.roots = s :=
+theorem roots_multiset_prod_x_sub_c (s : Multiset R) : (s.map fun a => X - C a).Prod.roots = s :=
   by
   rw [roots_multiset_prod, Multiset.bind_map]
   · simp_rw [roots_X_sub_C, Multiset.bind_singleton, Multiset.map_id']
@@ -735,7 +735,7 @@ theorem roots_multiset_prod_x_sub_c (s : Multiset R) : (s.map fun a => x - c a).
 
 @[simp]
 theorem natDegree_multiset_prod_x_sub_c_eq_card (s : Multiset R) :
-    (s.map fun a => x - c a).Prod.natDegree = s.card :=
+    (s.map fun a => X - C a).Prod.natDegree = s.card :=
   by
   rw [nat_degree_multiset_prod_of_monic, Multiset.map_map]
   ·
@@ -745,10 +745,10 @@ theorem natDegree_multiset_prod_x_sub_c_eq_card (s : Multiset R) :
 #align polynomial.nat_degree_multiset_prod_X_sub_C_eq_card Polynomial.natDegree_multiset_prod_x_sub_c_eq_card
 
 theorem card_roots_x_pow_sub_c {n : ℕ} (hn : 0 < n) (a : R) :
-    (roots ((x : R[X]) ^ n - c a)).card ≤ n :=
+    (roots ((X : R[X]) ^ n - C a)).card ≤ n :=
   WithBot.coe_le_coe.1 <|
     calc
-      ((roots ((x : R[X]) ^ n - c a)).card : WithBot ℕ) ≤ degree ((x : R[X]) ^ n - c a) :=
+      ((roots ((X : R[X]) ^ n - C a)).card : WithBot ℕ) ≤ degree ((X : R[X]) ^ n - C a) :=
         card_roots (x_pow_sub_c_ne_zero hn a)
       _ = n := degree_x_pow_sub_c hn a
       
@@ -758,7 +758,7 @@ section NthRoots
 
 /-- `nth_roots n a` noncomputably returns the solutions to `x ^ n = a`-/
 def nthRoots (n : ℕ) (a : R) : Multiset R :=
-  roots ((x : R[X]) ^ n - c a)
+  roots ((X : R[X]) ^ n - C a)
 #align polynomial.nth_roots Polynomial.nthRoots
 
 @[simp]
@@ -774,7 +774,7 @@ theorem nthRoots_zero (r : R) : nthRoots 0 r = 0 := by
 
 theorem card_nthRoots (n : ℕ) (a : R) : (nthRoots n a).card ≤ n :=
   if hn : n = 0 then
-    if h : (x : R[X]) ^ n - c a = 0 then by
+    if h : (X : R[X]) ^ n - C a = 0 then by
       simp only [Nat.zero_le, nth_roots, roots, h, dif_pos rfl, empty_eq_zero, card_zero]
     else
       WithBot.coe_le_coe.1
@@ -813,19 +813,19 @@ theorem Monic.comp (hp : p.Monic) (hq : q.Monic) (h : q.natDegree ≠ 0) : (p.co
   rw [monic.def, leading_coeff_comp h, monic.def.1 hp, monic.def.1 hq, one_pow, one_mul]
 #align polynomial.monic.comp Polynomial.Monic.comp
 
-theorem Monic.comp_x_add_c (hp : p.Monic) (r : R) : (p.comp (x + c r)).Monic :=
+theorem Monic.comp_x_add_c (hp : p.Monic) (r : R) : (p.comp (X + C r)).Monic :=
   by
   refine' hp.comp (monic_X_add_C _) fun ha => _
   rw [nat_degree_X_add_C] at ha
   exact one_ne_zero ha
 #align polynomial.monic.comp_X_add_C Polynomial.Monic.comp_x_add_c
 
-theorem Monic.comp_x_sub_c (hp : p.Monic) (r : R) : (p.comp (x - c r)).Monic := by
+theorem Monic.comp_x_sub_c (hp : p.Monic) (r : R) : (p.comp (X - C r)).Monic := by
   simpa using hp.comp_X_add_C (-r)
 #align polynomial.monic.comp_X_sub_C Polynomial.Monic.comp_x_sub_c
 
 theorem units_coeff_zero_smul (c : R[X]ˣ) (p : R[X]) : (c : R[X]).coeff 0 • p = c * p := by
-  rw [← Polynomial.c_mul', ← Polynomial.eq_c_of_degree_eq_zero (degree_coe_units c)]
+  rw [← Polynomial.C_mul', ← Polynomial.eq_c_of_degree_eq_zero (degree_coe_units c)]
 #align polynomial.units_coeff_zero_smul Polynomial.units_coeff_zero_smul
 
 @[simp]
@@ -833,7 +833,7 @@ theorem natDegree_coe_units (u : R[X]ˣ) : natDegree (u : R[X]) = 0 :=
   natDegree_eq_of_degree_eq_some (degree_coe_units u)
 #align polynomial.nat_degree_coe_units Polynomial.natDegree_coe_units
 
-theorem comp_eq_zero_iff : p.comp q = 0 ↔ p = 0 ∨ p.eval (q.coeff 0) = 0 ∧ q = c (q.coeff 0) :=
+theorem comp_eq_zero_iff : p.comp q = 0 ↔ p = 0 ∨ p.eval (q.coeff 0) = 0 ∧ q = C (q.coeff 0) :=
   by
   constructor
   · intro h
@@ -881,7 +881,7 @@ theorem rootSet_def (p : T[X]) (S) [CommRing S] [IsDomain S] [Algebra T S] :
 #align polynomial.root_set_def Polynomial.rootSet_def
 
 @[simp]
-theorem rootSet_c [CommRing S] [IsDomain S] [Algebra T S] (a : T) : (c a).rootSet S = ∅ := by
+theorem rootSet_c [CommRing S] [IsDomain S] [Algebra T S] (a : T) : (C a).rootSet S = ∅ := by
   rw [root_set_def, map_C, roots_C, Multiset.toFinset_zero, Finset.coe_empty]
 #align polynomial.root_set_C Polynomial.rootSet_c
 
@@ -981,11 +981,11 @@ theorem degree_eq_degree_of_associated (h : Associated p q) : degree p = degree
 theorem degree_eq_one_of_irreducible_of_root (hi : Irreducible p) {x : R} (hx : IsRoot p x) :
     degree p = 1 :=
   let ⟨g, hg⟩ := dvd_iff_isRoot.2 hx
-  have : IsUnit (x - c x) ∨ IsUnit g := hi.isUnit_or_isUnit hg
+  have : IsUnit (X - C x) ∨ IsUnit g := hi.isUnit_or_isUnit hg
   this.elim
     (fun h => by
-      have h₁ : degree (x - c x) = 1 := degree_x_sub_c x
-      have h₂ : degree (x - c x) = 0 := degree_eq_zero_of_isUnit h
+      have h₁ : degree (X - C x) = 1 := degree_x_sub_c x
+      have h₂ : degree (X - C x) = 0 := degree_eq_zero_of_isUnit h
       rw [h₁] at h₂ <;> exact absurd h₂ (by decide))
     fun hgu => by rw [hg, degree_mul, degree_X_sub_C, degree_eq_zero_of_is_unit hgu, add_zero]
 #align polynomial.degree_eq_one_of_irreducible_of_root Polynomial.degree_eq_one_of_irreducible_of_root
@@ -1005,7 +1005,7 @@ theorem leadingCoeff_divByMonic_of_monic {R : Type u} [CommRing R] {p q : R[X]}
 #align polynomial.leading_coeff_div_by_monic_of_monic Polynomial.leadingCoeff_divByMonic_of_monic
 
 theorem leadingCoeff_divByMonic_x_sub_c (p : R[X]) (hp : degree p ≠ 0) (a : R) :
-    leadingCoeff (p /ₘ (x - c a)) = leadingCoeff p :=
+    leadingCoeff (p /ₘ (X - C a)) = leadingCoeff p :=
   by
   nontriviality
   cases' hp.lt_or_lt with hd hd
@@ -1015,7 +1015,7 @@ theorem leadingCoeff_divByMonic_x_sub_c (p : R[X]) (hp : degree p ≠ 0) (a : R)
 #align polynomial.leading_coeff_div_by_monic_X_sub_C Polynomial.leadingCoeff_divByMonic_x_sub_c
 
 theorem eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le {R} [CommRing R] {p q : R[X]}
-    (hp : p.Monic) (hdiv : p ∣ q) (hdeg : q.natDegree ≤ p.natDegree) : q = c q.leadingCoeff * p :=
+    (hp : p.Monic) (hdiv : p ∣ q) (hdeg : q.natDegree ≤ p.natDegree) : q = C q.leadingCoeff * p :=
   by
   obtain ⟨r, hr⟩ := hdiv
   obtain rfl | hq := eq_or_ne q 0; · simp
@@ -1038,8 +1038,8 @@ theorem eq_of_monic_of_dvd_of_natDegree_le {R} [CommRing R] {p q : R[X]} (hp : p
 #align polynomial.eq_of_monic_of_dvd_of_nat_degree_le Polynomial.eq_of_monic_of_dvd_of_natDegree_le
 
 theorem isCoprime_x_sub_c_of_isUnit_sub {R} [CommRing R] {a b : R} (h : IsUnit (a - b)) :
-    IsCoprime (x - c a) (x - c b) :=
-  ⟨-c h.Unit⁻¹.val, c h.Unit⁻¹.val,
+    IsCoprime (X - C a) (X - C b) :=
+  ⟨-C h.Unit⁻¹.val, C h.Unit⁻¹.val,
     by
     rw [neg_mul_comm, ← left_distrib, neg_add_eq_sub, sub_sub_sub_cancel_left, ← C_sub, ← C_mul]
     convert C_1
@@ -1047,22 +1047,22 @@ theorem isCoprime_x_sub_c_of_isUnit_sub {R} [CommRing R] {a b : R} (h : IsUnit (
 #align polynomial.is_coprime_X_sub_C_of_is_unit_sub Polynomial.isCoprime_x_sub_c_of_isUnit_sub
 
 theorem pairwise_coprime_x_sub_c {K} [Field K] {I : Type v} {s : I → K} (H : Function.Injective s) :
-    Pairwise (IsCoprime on fun i : I => x - c (s i)) := fun i j hij =>
+    Pairwise (IsCoprime on fun i : I => X - C (s i)) := fun i j hij =>
   isCoprime_x_sub_c_of_isUnit_sub (sub_ne_zero_of_ne <| H.Ne hij).IsUnit
 #align polynomial.pairwise_coprime_X_sub_C Polynomial.pairwise_coprime_x_sub_c
 
-theorem monic_prod_multiset_x_sub_c : Monic (p.roots.map fun a => x - c a).Prod :=
+theorem monic_prod_multiset_x_sub_c : Monic (p.roots.map fun a => X - C a).Prod :=
   monic_multiset_prod_of_monic _ _ fun a _ => monic_x_sub_c a
 #align polynomial.monic_prod_multiset_X_sub_C Polynomial.monic_prod_multiset_x_sub_c
 
 theorem prod_multiset_root_eq_finset_root :
-    (p.roots.map fun a => x - c a).Prod =
-      p.roots.toFinset.Prod fun a => (x - c a) ^ rootMultiplicity a p :=
+    (p.roots.map fun a => X - C a).Prod =
+      p.roots.toFinset.Prod fun a => (X - C a) ^ rootMultiplicity a p :=
   by simp only [count_roots, Finset.prod_multiset_map_count]
 #align polynomial.prod_multiset_root_eq_finset_root Polynomial.prod_multiset_root_eq_finset_root
 
 /-- The product `∏ (X - a)` for `a` inside the multiset `p.roots` divides `p`. -/
-theorem prod_multiset_x_sub_c_dvd (p : R[X]) : (p.roots.map fun a => x - c a).Prod ∣ p :=
+theorem prod_multiset_x_sub_c_dvd (p : R[X]) : (p.roots.map fun a => X - C a).Prod ∣ p :=
   by
   rw [← map_dvd_map _ (IsFractionRing.injective R <| FractionRing R) monic_prod_multiset_X_sub_C]
   rw [prod_multiset_root_eq_finset_root, Polynomial.map_prod]
@@ -1074,7 +1074,7 @@ theorem prod_multiset_x_sub_c_dvd (p : R[X]) : (p.roots.map fun a => x - c a).Pr
 
 /-- A Galois connection. -/
 theorem Multiset.prod_x_sub_c_dvd_iff_le_roots {p : R[X]} (hp : p ≠ 0) (s : Multiset R) :
-    (s.map fun a => x - c a).Prod ∣ p ↔ s ≤ p.roots :=
+    (s.map fun a => X - C a).Prod ∣ p ↔ s ≤ p.roots :=
   ⟨fun h =>
     Multiset.le_iff_count.2 fun r =>
       by
@@ -1087,7 +1087,7 @@ theorem Multiset.prod_x_sub_c_dvd_iff_le_roots {p : R[X]} (hp : p ≠ 0) (s : Mu
 
 theorem exists_prod_multiset_x_sub_c_mul (p : R[X]) :
     ∃ q,
-      (p.roots.map fun a => x - c a).Prod * q = p ∧
+      (p.roots.map fun a => X - C a).Prod * q = p ∧
         p.roots.card + q.natDegree = p.natDegree ∧ q.roots = 0 :=
   by
   obtain ⟨q, he⟩ := p.prod_multiset_X_sub_C_dvd
@@ -1107,7 +1107,7 @@ theorem exists_prod_multiset_x_sub_c_mul (p : R[X]) :
 /-- A polynomial `p` that has as many roots as its degree
 can be written `p = p.leading_coeff * ∏(X - a)`, for `a` in `p.roots`. -/
 theorem c_leadingCoeff_mul_prod_multiset_x_sub_c (hroots : p.roots.card = p.natDegree) :
-    c p.leadingCoeff * (p.roots.map fun a => x - c a).Prod = p :=
+    C p.leadingCoeff * (p.roots.map fun a => X - C a).Prod = p :=
   (eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le monic_prod_multiset_x_sub_c
       p.prod_multiset_x_sub_c_dvd
       ((natDegree_multiset_prod_x_sub_c_eq_card _).trans hroots).ge).symm
@@ -1116,7 +1116,7 @@ theorem c_leadingCoeff_mul_prod_multiset_x_sub_c (hroots : p.roots.card = p.natD
 /-- A monic polynomial `p` that has as many roots as its degree
 can be written `p = ∏(X - a)`, for `a` in `p.roots`. -/
 theorem prod_multiset_x_sub_c_of_monic_of_roots_card_eq (hp : p.Monic)
-    (hroots : p.roots.card = p.natDegree) : (p.roots.map fun a => x - c a).Prod = p :=
+    (hroots : p.roots.card = p.natDegree) : (p.roots.map fun a => X - C a).Prod = p :=
   by
   convert C_leading_coeff_mul_prod_multiset_X_sub_C hroots
   rw [hp.leading_coeff, C_1, one_mul]

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

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

@@ -338,22 +338,23 @@ theorem Monic.not_irreducible_iff_exists_add_mul_eq_coeff (hm : p.Monic) (hnd :
   cases subsingleton_or_nontrivial R
   · simp [natDegree_of_subsingleton] at hnd
   rw [hm.irreducible_iff_natDegree', and_iff_right, hnd]
-  push_neg; constructor
-  · rintro ⟨a, b, ha, hb, rfl, hdb⟩
-    simp only [zero_lt_two, Nat.div_self, ge_iff_le,
-      Nat.Ioc_succ_singleton, zero_add, mem_singleton] at hdb
-    have hda := hnd
-    rw [ha.natDegree_mul hb, hdb] at hda
-    use a.coeff 0, b.coeff 0, mul_coeff_zero a b
-    simpa only [nextCoeff, hnd, add_right_cancel hda, hdb] using ha.nextCoeff_mul hb
-  · rintro ⟨c₁, c₂, hmul, hadd⟩
-    refine
-      ⟨X + C c₁, X + C c₂, monic_X_add_C _, monic_X_add_C _, ?_, ?_⟩
-    · rw [p.as_sum_range_C_mul_X_pow, hnd, Finset.sum_range_succ, Finset.sum_range_succ,
-        Finset.sum_range_one, ← hnd, hm.coeff_natDegree, hnd, hmul, hadd, C_mul, C_add, C_1]
-      ring
-    · rw [mem_Ioc, natDegree_X_add_C _]
-      simp
+  · push_neg
+    constructor
+    · rintro ⟨a, b, ha, hb, rfl, hdb⟩
+      simp only [zero_lt_two, Nat.div_self, ge_iff_le,
+        Nat.Ioc_succ_singleton, zero_add, mem_singleton] at hdb
+      have hda := hnd
+      rw [ha.natDegree_mul hb, hdb] at hda
+      use a.coeff 0, b.coeff 0, mul_coeff_zero a b
+      simpa only [nextCoeff, hnd, add_right_cancel hda, hdb] using ha.nextCoeff_mul hb
+    · rintro ⟨c₁, c₂, hmul, hadd⟩
+      refine
+        ⟨X + C c₁, X + C c₂, monic_X_add_C _, monic_X_add_C _, ?_, ?_⟩
+      · rw [p.as_sum_range_C_mul_X_pow, hnd, Finset.sum_range_succ, Finset.sum_range_succ,
+          Finset.sum_range_one, ← hnd, hm.coeff_natDegree, hnd, hmul, hadd, C_mul, C_add, C_1]
+        ring
+      · rw [mem_Ioc, natDegree_X_add_C _]
+        simp
   · rintro rfl
     simp [natDegree_one] at hnd
 #align polynomial.monic.not_irreducible_iff_exists_add_mul_eq_coeff Polynomial.Monic.not_irreducible_iff_exists_add_mul_eq_coeff
@@ -1616,7 +1617,7 @@ theorem isUnit_of_isUnit_leadingCoeff_of_isUnit_map {f : R[X]} (hf : IsUnit f.le
     convert hf
     change coeff f 0 = coeff f (natDegree f)
     rw [(degree_eq_iff_natDegree_eq _).1 dz]
-    rfl
+    · rfl
     rintro rfl
     simp at H
   · intro h

and reduce its scope in a few other instances. Mostly in CategoryTheory and Data this time; some Combinatorics also.

Co-authored-by: Richard Osborn <richardosborn@mac.com>

@@ -30,9 +30,6 @@ This file starts looking like the ring theory of $R[X]$
 
 -/
 
-set_option autoImplicit true
-
-
 noncomputable section
 
 open Polynomial
@@ -738,7 +735,7 @@ theorem isRoot_of_mem_roots (h : a ∈ p.roots) : IsRoot p a :=
 #align polynomial.is_root_of_mem_roots Polynomial.isRoot_of_mem_roots
 
 -- Porting note: added during port.
-lemma mem_roots_iff_aeval_eq_zero (w : p ≠ 0) : x ∈ roots p ↔ aeval x p = 0 := by
+lemma mem_roots_iff_aeval_eq_zero {x : R} (w : p ≠ 0) : x ∈ roots p ↔ aeval x p = 0 := by
   rw [mem_roots w, IsRoot.def, aeval_def, eval₂_eq_eval_map]
   simp
 

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

@@ -570,7 +570,7 @@ open Multiset
 
 theorem prime_X_sub_C (r : R) : Prime (X - C r) :=
   ⟨X_sub_C_ne_zero r, not_isUnit_X_sub_C r, fun _ _ => by
-    simp_rw [dvd_iff_isRoot, IsRoot.definition, eval_mul, mul_eq_zero]
+    simp_rw [dvd_iff_isRoot, IsRoot.def, eval_mul, mul_eq_zero]
     exact id⟩
 set_option linter.uppercaseLean3 false in
 #align polynomial.prime_X_sub_C Polynomial.prime_X_sub_C
@@ -739,7 +739,7 @@ theorem isRoot_of_mem_roots (h : a ∈ p.roots) : IsRoot p a :=
 
 -- Porting note: added during port.
 lemma mem_roots_iff_aeval_eq_zero (w : p ≠ 0) : x ∈ roots p ↔ aeval x p = 0 := by
-  rw [mem_roots w, IsRoot.definition, aeval_def, eval₂_eq_eval_map]
+  rw [mem_roots w, IsRoot.def, aeval_def, eval₂_eq_eval_map]
   simp
 
 theorem card_le_degree_of_subset_roots {p : R[X]} {Z : Finset R} (h : Z.val ⊆ p.roots) :
@@ -784,7 +784,7 @@ theorem roots.le_of_dvd (h : q ≠ 0) : p ∣ q → roots p ≤ roots q := by
 #align polynomial.roots.le_of_dvd Polynomial.roots.le_of_dvd
 
 theorem mem_roots_sub_C' {p : R[X]} {a x : R} : x ∈ (p - C a).roots ↔ p ≠ C a ∧ p.eval x = a := by
-  rw [mem_roots', IsRoot.definition, sub_ne_zero, eval_sub, sub_eq_zero, eval_C]
+  rw [mem_roots', IsRoot.def, sub_ne_zero, eval_sub, sub_eq_zero, eval_C]
 set_option linter.uppercaseLean3 false in
 #align polynomial.mem_roots_sub_C' Polynomial.mem_roots_sub_C'
 
@@ -932,7 +932,7 @@ def nthRoots (n : ℕ) (a : R) : Multiset R :=
 
 @[simp]
 theorem mem_nthRoots {n : ℕ} (hn : 0 < n) {a x : R} : x ∈ nthRoots n a ↔ x ^ n = a := by
-  rw [nthRoots, mem_roots (X_pow_sub_C_ne_zero hn a), IsRoot.definition, eval_sub, eval_C, eval_pow,
+  rw [nthRoots, mem_roots (X_pow_sub_C_ne_zero hn a), IsRoot.def, eval_sub, eval_C, eval_pow,
     eval_X, sub_eq_zero]
 #align polynomial.mem_nth_roots Polynomial.mem_nthRoots
 
@@ -1018,7 +1018,7 @@ theorem one_mem_nthRootsFinset (hn : 0 < n) : 1 ∈ nthRootsFinset n R := by
 end NthRoots
 
 theorem Monic.comp (hp : p.Monic) (hq : q.Monic) (h : q.natDegree ≠ 0) : (p.comp q).Monic := by
-  rw [Monic.def', leadingCoeff_comp h, Monic.def'.1 hp, Monic.def'.1 hq, one_pow, one_mul]
+  rw [Monic.def, leadingCoeff_comp h, Monic.def.1 hp, Monic.def.1 hq, one_pow, one_mul]
 #align polynomial.monic.comp Polynomial.Monic.comp
 
 theorem Monic.comp_X_add_C (hp : p.Monic) (r : R) : (p.comp (X + C r)).Monic := by
@@ -1084,7 +1084,7 @@ theorem aroots_def (p : T[X]) (S) [CommRing S] [IsDomain S] [Algebra T S] :
 
 theorem mem_aroots' [CommRing S] [IsDomain S] [Algebra T S] {p : T[X]} {a : S} :
     a ∈ p.aroots S ↔ p.map (algebraMap T S) ≠ 0 ∧ aeval a p = 0 := by
-  rw [mem_roots', IsRoot.definition, ← eval₂_eq_eval_map, aeval_def]
+  rw [mem_roots', IsRoot.def, ← eval₂_eq_eval_map, aeval_def]
 
 theorem mem_aroots [CommRing S] [IsDomain S] [Algebra T S]
     [NoZeroSMulDivisors T S] {p : T[X]} {a : S} : a ∈ p.aroots S ↔ p ≠ 0 ∧ aeval a p = 0 := by
@@ -1383,7 +1383,7 @@ lemma eq_zero_of_natDegree_lt_card_of_eval_eq_zero {R} [CommRing R] [IsDomain R]
     _ ≤ Finset.card p.roots.toFinset := Finset.card_mono ?_
   intro _
   simp only [Finset.mem_image, Finset.mem_univ, true_and, Multiset.mem_toFinset, mem_roots', ne_eq,
-    IsRoot.definition, forall_exists_index, hp, not_false_eq_true]
+    IsRoot.def, forall_exists_index, hp, not_false_eq_true]
   rintro x rfl
   exact heval _
 

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

@@ -3,11 +3,11 @@ Copyright (c) 2018 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker, Johan Commelin
 -/
-import Mathlib.Data.Polynomial.AlgebraMap
-import Mathlib.Data.Polynomial.Degree.Lemmas
-import Mathlib.Data.Polynomial.Div
-import Mathlib.RingTheory.Localization.FractionRing
+import Mathlib.Algebra.Polynomial.AlgebraMap
 import Mathlib.Algebra.Polynomial.BigOperators
+import Mathlib.Algebra.Polynomial.Degree.Lemmas
+import Mathlib.Algebra.Polynomial.Div
+import Mathlib.RingTheory.Localization.FractionRing
 
 #align_import data.polynomial.ring_division from "leanprover-community/mathlib"@"8efcf8022aac8e01df8d302dcebdbc25d6a886c8"
 
@@ -418,7 +418,7 @@ variable [CommRing R]
 
 /- Porting note: the ML3 proof no longer worked because of a conflict in the
 inferred type and synthesized type for `DecidableRel` when using `Nat.le_find_iff` from
-`Mathlib.Data.Polynomial.Div` After some discussion on [Zulip]
+`Mathlib.Algebra.Polynomial.Div` After some discussion on [Zulip]
 (https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/decidability.20leakage)
 introduced `Polynomial.rootMultiplicity_eq_nat_find_of_nonzero` to contain the issue
 -/

@@ -158,7 +158,7 @@ theorem natDegree_pow (p : R[X]) (n : ℕ) : natDegree (p ^ n) = n * natDegree p
   obtain rfl | hp := eq_or_ne p 0
   · obtain rfl | hn := eq_or_ne n 0 <;> simp [*]
   exact natDegree_pow' $ by
-    rw [← leadingCoeff_pow, Ne.def, leadingCoeff_eq_zero]; exact pow_ne_zero _ hp
+    rw [← leadingCoeff_pow, Ne, leadingCoeff_eq_zero]; exact pow_ne_zero _ hp
 #align polynomial.nat_degree_pow Polynomial.natDegree_pow
 
 theorem degree_le_mul_left (p : R[X]) (hq : q ≠ 0) : degree p ≤ degree (p * q) := by
@@ -825,7 +825,7 @@ theorem roots_one : (1 : R[X]).roots = ∅ :=
 @[simp]
 theorem roots_C_mul (p : R[X]) (ha : a ≠ 0) : (C a * p).roots = p.roots := by
   by_cases hp : p = 0 <;>
-    simp only [roots_mul, *, Ne.def, mul_eq_zero, C_eq_zero, or_self_iff, not_false_iff, roots_C,
+    simp only [roots_mul, *, Ne, mul_eq_zero, C_eq_zero, or_self_iff, not_false_iff, roots_C,
       zero_add, mul_zero]
 set_option linter.uppercaseLean3 false in
 #align polynomial.roots_C_mul Polynomial.roots_C_mul
@@ -1271,7 +1271,7 @@ end Roots
 
 theorem coeff_coe_units_zero_ne_zero (u : R[X]ˣ) : coeff (u : R[X]) 0 ≠ 0 := by
   conv in 0 => rw [← natDegree_coe_units u]
-  rw [← leadingCoeff, Ne.def, leadingCoeff_eq_zero]
+  rw [← leadingCoeff, Ne, leadingCoeff_eq_zero]
   exact Units.ne_zero _
 #align polynomial.coeff_coe_units_zero_ne_zero Polynomial.coeff_coe_units_zero_ne_zero
 

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

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

where the latter is more natural

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

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

but it seems to no longer apply.

Remarks on the PR :

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

@@ -864,7 +864,7 @@ theorem roots_pow (p : R[X]) (n : ℕ) : (p ^ n).roots = n • p.roots := by
   · rw [pow_zero, roots_one, Nat.zero_eq, zero_smul, empty_eq_zero]
   · rcases eq_or_ne p 0 with (rfl | hp)
     · rw [zero_pow n.succ_ne_zero, roots_zero, smul_zero]
-    · rw [pow_succ', roots_mul (mul_ne_zero (pow_ne_zero _ hp) hp), ihn, Nat.succ_eq_add_one,
+    · rw [pow_succ, roots_mul (mul_ne_zero (pow_ne_zero _ hp) hp), ihn, Nat.succ_eq_add_one,
         add_smul, one_smul]
 #align polynomial.roots_pow Polynomial.roots_pow
 

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

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

| Statement | New name | Old name | |

@@ -490,8 +490,8 @@ theorem eval_divByMonic_eq_trailingCoeff_comp {p : R[X]} {t : R} :
   have : (g.comp (X + C t)).coeff 0 = g.eval t := by
     rw [coeff_zero_eq_eval_zero, eval_comp, eval_add, eval_X, eval_C, zero_add]
   rw [← congr_arg (comp · <| X + C t) mul_eq, mul_comp, pow_comp, sub_comp, X_comp, C_comp,
-    add_sub_cancel, ← reverse_leadingCoeff, reverse_X_pow_mul, reverse_leadingCoeff, trailingCoeff,
-    Nat.le_zero.mp (natTrailingDegree_le_of_ne_zero <|
+    add_sub_cancel_right, ← reverse_leadingCoeff, reverse_X_pow_mul, reverse_leadingCoeff,
+    trailingCoeff, Nat.le_zero.1 (natTrailingDegree_le_of_ne_zero <|
       this ▸ eval_divByMonic_pow_rootMultiplicity_ne_zero t hp), this]
 
 section nonZeroDivisors

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

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

@@ -570,7 +570,7 @@ open Multiset
 
 theorem prime_X_sub_C (r : R) : Prime (X - C r) :=
   ⟨X_sub_C_ne_zero r, not_isUnit_X_sub_C r, fun _ _ => by
-    simp_rw [dvd_iff_isRoot, IsRoot.def, eval_mul, mul_eq_zero]
+    simp_rw [dvd_iff_isRoot, IsRoot.definition, eval_mul, mul_eq_zero]
     exact id⟩
 set_option linter.uppercaseLean3 false in
 #align polynomial.prime_X_sub_C Polynomial.prime_X_sub_C
@@ -739,7 +739,7 @@ theorem isRoot_of_mem_roots (h : a ∈ p.roots) : IsRoot p a :=
 
 -- Porting note: added during port.
 lemma mem_roots_iff_aeval_eq_zero (w : p ≠ 0) : x ∈ roots p ↔ aeval x p = 0 := by
-  rw [mem_roots w, IsRoot.def, aeval_def, eval₂_eq_eval_map]
+  rw [mem_roots w, IsRoot.definition, aeval_def, eval₂_eq_eval_map]
   simp
 
 theorem card_le_degree_of_subset_roots {p : R[X]} {Z : Finset R} (h : Z.val ⊆ p.roots) :
@@ -784,7 +784,7 @@ theorem roots.le_of_dvd (h : q ≠ 0) : p ∣ q → roots p ≤ roots q := by
 #align polynomial.roots.le_of_dvd Polynomial.roots.le_of_dvd
 
 theorem mem_roots_sub_C' {p : R[X]} {a x : R} : x ∈ (p - C a).roots ↔ p ≠ C a ∧ p.eval x = a := by
-  rw [mem_roots', IsRoot.def, sub_ne_zero, eval_sub, sub_eq_zero, eval_C]
+  rw [mem_roots', IsRoot.definition, sub_ne_zero, eval_sub, sub_eq_zero, eval_C]
 set_option linter.uppercaseLean3 false in
 #align polynomial.mem_roots_sub_C' Polynomial.mem_roots_sub_C'
 
@@ -932,7 +932,7 @@ def nthRoots (n : ℕ) (a : R) : Multiset R :=
 
 @[simp]
 theorem mem_nthRoots {n : ℕ} (hn : 0 < n) {a x : R} : x ∈ nthRoots n a ↔ x ^ n = a := by
-  rw [nthRoots, mem_roots (X_pow_sub_C_ne_zero hn a), IsRoot.def, eval_sub, eval_C, eval_pow,
+  rw [nthRoots, mem_roots (X_pow_sub_C_ne_zero hn a), IsRoot.definition, eval_sub, eval_C, eval_pow,
     eval_X, sub_eq_zero]
 #align polynomial.mem_nth_roots Polynomial.mem_nthRoots
 
@@ -1018,7 +1018,7 @@ theorem one_mem_nthRootsFinset (hn : 0 < n) : 1 ∈ nthRootsFinset n R := by
 end NthRoots
 
 theorem Monic.comp (hp : p.Monic) (hq : q.Monic) (h : q.natDegree ≠ 0) : (p.comp q).Monic := by
-  rw [Monic.def, leadingCoeff_comp h, Monic.def.1 hp, Monic.def.1 hq, one_pow, one_mul]
+  rw [Monic.def', leadingCoeff_comp h, Monic.def'.1 hp, Monic.def'.1 hq, one_pow, one_mul]
 #align polynomial.monic.comp Polynomial.Monic.comp
 
 theorem Monic.comp_X_add_C (hp : p.Monic) (r : R) : (p.comp (X + C r)).Monic := by
@@ -1084,7 +1084,7 @@ theorem aroots_def (p : T[X]) (S) [CommRing S] [IsDomain S] [Algebra T S] :
 
 theorem mem_aroots' [CommRing S] [IsDomain S] [Algebra T S] {p : T[X]} {a : S} :
     a ∈ p.aroots S ↔ p.map (algebraMap T S) ≠ 0 ∧ aeval a p = 0 := by
-  rw [mem_roots', IsRoot.def, ← eval₂_eq_eval_map, aeval_def]
+  rw [mem_roots', IsRoot.definition, ← eval₂_eq_eval_map, aeval_def]
 
 theorem mem_aroots [CommRing S] [IsDomain S] [Algebra T S]
     [NoZeroSMulDivisors T S] {p : T[X]} {a : S} : a ∈ p.aroots S ↔ p ≠ 0 ∧ aeval a p = 0 := by
@@ -1383,7 +1383,7 @@ lemma eq_zero_of_natDegree_lt_card_of_eval_eq_zero {R} [CommRing R] [IsDomain R]
     _ ≤ Finset.card p.roots.toFinset := Finset.card_mono ?_
   intro _
   simp only [Finset.mem_image, Finset.mem_univ, true_and, Multiset.mem_toFinset, mem_roots', ne_eq,
-    IsRoot.def, forall_exists_index, hp, not_false_eq_true]
+    IsRoot.definition, forall_exists_index, hp, not_false_eq_true]
   rintro x rfl
   exact heval _
 

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

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

@@ -975,7 +975,7 @@ def nthRootsFinset (n : ℕ) (R : Type*) [CommRing R] [IsDomain R] : Finset R :=
   Multiset.toFinset (nthRoots n (1 : R))
 #align polynomial.nth_roots_finset Polynomial.nthRootsFinset
 
--- Porting note: new
+-- Porting note (#10756): new lemma
 lemma nthRootsFinset_def (n : ℕ) (R : Type*) [CommRing R] [IsDomain R] [DecidableEq R] :
     nthRootsFinset n R = Multiset.toFinset (nthRoots n (1 : R)) := by
   unfold nthRootsFinset

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

@@ -533,7 +533,7 @@ theorem rootMultiplicity_X_sub_C_self [Nontrivial R] {x : R} :
 set_option linter.uppercaseLean3 false in
 #align polynomial.root_multiplicity_X_sub_C_self Polynomial.rootMultiplicity_X_sub_C_self
 
--- porting note: swapped instance argument order
+-- Porting note: swapped instance argument order
 theorem rootMultiplicity_X_sub_C [Nontrivial R] [DecidableEq R] {x y : R} :
     rootMultiplicity x (X - C y) = if x = y then 1 else 0 := by
   split_ifs with hxy
@@ -975,7 +975,7 @@ def nthRootsFinset (n : ℕ) (R : Type*) [CommRing R] [IsDomain R] : Finset R :=
   Multiset.toFinset (nthRoots n (1 : R))
 #align polynomial.nth_roots_finset Polynomial.nthRootsFinset
 
--- porting note: new
+-- Porting note: new
 lemma nthRootsFinset_def (n : ℕ) (R : Type*) [CommRing R] [IsDomain R] [DecidableEq R] :
     nthRootsFinset n R = Multiset.toFinset (nthRoots n (1 : R)) := by
   unfold nthRootsFinset

These did not respect the naming convention by having the coe as a prefix instead of a suffix, or vice-versa. Also add a bunch of norm_cast

@@ -849,7 +849,7 @@ theorem roots_list_prod (L : List R[X]) :
 
 theorem roots_multiset_prod (m : Multiset R[X]) : (0 : R[X]) ∉ m → m.prod.roots = m.bind roots := by
   rcases m with ⟨L⟩
-  simpa only [Multiset.coe_prod, quot_mk_to_coe''] using roots_list_prod L
+  simpa only [Multiset.prod_coe, quot_mk_to_coe''] using roots_list_prod L
 #align polynomial.roots_multiset_prod Polynomial.roots_multiset_prod
 
 theorem roots_prod {ι : Type*} (f : ι → R[X]) (s : Finset ι) :

@@ -1394,15 +1394,20 @@ lemma eq_zero_of_natDegree_lt_card_of_eval_eq_zero' {R} [CommRing R] [IsDomain R
     (fun i : s ↦ heval i i.prop) (hcard.trans_eq (Fintype.card_coe s).symm)
 
 open Cardinal in
-lemma exists_eval_ne_zero_of_natDegree_lt_card (f : R[X]) (hf : f ≠ 0) (hfR : f.natDegree < #R) :
-    ∃ r, f.eval r ≠ 0 := by
-  contrapose! hf
+lemma eq_zero_of_forall_eval_zero_of_natDegree_lt_card
+    (f : R[X]) (hf : ∀ r, f.eval r = 0) (hfR : f.natDegree < #R) : f = 0 := by
   obtain hR|hR := finite_or_infinite R
   · have := Fintype.ofFinite R
     apply eq_zero_of_natDegree_lt_card_of_eval_eq_zero f Function.injective_id hf
-    aesop
+    simpa only [mk_fintype, Nat.cast_lt] using hfR
   · exact zero_of_eval_zero _ hf
 
+open Cardinal in
+lemma exists_eval_ne_zero_of_natDegree_lt_card (f : R[X]) (hf : f ≠ 0) (hfR : f.natDegree < #R) :
+    ∃ r, f.eval r ≠ 0 := by
+  contrapose! hf
+  exact eq_zero_of_forall_eval_zero_of_natDegree_lt_card f hf hfR
+
 theorem isCoprime_X_sub_C_of_isUnit_sub {R} [CommRing R] {a b : R} (h : IsUnit (a - b)) :
     IsCoprime (X - C a) (X - C b) :=
   ⟨-C h.unit⁻¹.val, C h.unit⁻¹.val, by

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

This follows on from #6964.

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

@@ -487,8 +487,8 @@ theorem eval_divByMonic_eq_trailingCoeff_comp {p : R[X]} {t : R} :
   have mul_eq := p.pow_mul_divByMonic_rootMultiplicity_eq t
   set m := p.rootMultiplicity t
   set g := p /ₘ (X - C t) ^ m
-  have : (g.comp (X + C t)).coeff 0 = g.eval t
-  · rw [coeff_zero_eq_eval_zero, eval_comp, eval_add, eval_X, eval_C, zero_add]
+  have : (g.comp (X + C t)).coeff 0 = g.eval t := by
+    rw [coeff_zero_eq_eval_zero, eval_comp, eval_add, eval_X, eval_C, zero_add]
   rw [← congr_arg (comp · <| X + C t) mul_eq, mul_comp, pow_comp, sub_comp, X_comp, C_comp,
     add_sub_cancel, ← reverse_leadingCoeff, reverse_X_pow_mul, reverse_leadingCoeff, trailingCoeff,
     Nat.le_zero.mp (natTrailingDegree_le_of_ne_zero <|
@@ -1094,8 +1094,8 @@ theorem mem_aroots [CommRing S] [IsDomain S] [Algebra T S]
 theorem aroots_mul [CommRing S] [IsDomain S] [Algebra T S]
     [NoZeroSMulDivisors T S] {p q : T[X]} (hpq : p * q ≠ 0) :
     (p * q).aroots S = p.aroots S + q.aroots S := by
-  suffices : map (algebraMap T S) p * map (algebraMap T S) q ≠ 0
-  · rw [aroots_def, Polynomial.map_mul, roots_mul this]
+  suffices map (algebraMap T S) p * map (algebraMap T S) q ≠ 0 by
+    rw [aroots_def, Polynomial.map_mul, roots_mul this]
   rwa [← Polynomial.map_mul, Polynomial.map_ne_zero_iff
     (NoZeroSMulDivisors.algebraMap_injective T S)]
 

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

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

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

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

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

@@ -239,6 +239,17 @@ theorem isUnit_iff : IsUnit p ↔ ∃ r : R, IsUnit r ∧ C r = p :=
     fun ⟨_, hr, hrp⟩ => hrp ▸ isUnit_C.2 hr⟩
 #align polynomial.is_unit_iff Polynomial.isUnit_iff
 
+theorem not_isUnit_of_degree_pos (p : R[X])
+    (hpl : 0 < p.degree) : ¬ IsUnit p := by
+  cases subsingleton_or_nontrivial R
+  · simp [Subsingleton.elim p 0] at hpl
+  intro h
+  simp [degree_eq_zero_of_isUnit h] at hpl
+
+theorem not_isUnit_of_natDegree_pos (p : R[X])
+    (hpl : 0 < p.natDegree) : ¬ IsUnit p :=
+  not_isUnit_of_degree_pos _ (natDegree_pos_iff_degree_pos.mp hpl)
+
 variable [CharZero R]
 
 -- Porting note: bit0/bit1 are deprecated
@@ -314,6 +325,17 @@ theorem Monic.irreducible_iff_natDegree' (hp : p.Monic) : Irreducible p ↔ p 
     · exact ⟨f, g, hf, hg, rfl, h.2, add_le_add_right hl _⟩
 #align polynomial.monic.irreducible_iff_nat_degree' Polynomial.Monic.irreducible_iff_natDegree'
 
+/-- Alternate phrasing of `Polynomial.Monic.irreducible_iff_natDegree'` where we only have to check
+one divisor at a time. -/
+theorem Monic.irreducible_iff_lt_natDegree_lt {p : R[X]} (hp : p.Monic) (hp1 : p ≠ 1) :
+    Irreducible p ↔ ∀ q, Monic q → natDegree q ∈ Finset.Ioc 0 (natDegree p / 2) → ¬ q ∣ p := by
+  rw [hp.irreducible_iff_natDegree', and_iff_right hp1]
+  constructor
+  · rintro h g hg hdg ⟨f, rfl⟩
+    exact h f g (hg.of_mul_monic_left hp) hg (mul_comm f g) hdg
+  · rintro h f g - hg rfl hdg
+    exact h g hg hdg (dvd_mul_left g f)
+
 theorem Monic.not_irreducible_iff_exists_add_mul_eq_coeff (hm : p.Monic) (hnd : p.natDegree = 2) :
     ¬Irreducible p ↔ ∃ c₁ c₂, p.coeff 0 = c₁ * c₂ ∧ p.coeff 1 = c₁ + c₂ := by
   cases subsingleton_or_nontrivial R
@@ -358,6 +380,38 @@ instance : IsDomain R[X] :=
 
 end Ring
 
+section CommSemiring
+
+variable [CommSemiring R]
+
+theorem Monic.C_dvd_iff_isUnit {p : R[X]} (hp : Monic p) {a : R} :
+    C a ∣ p ↔ IsUnit a :=
+  ⟨fun h => isUnit_iff_dvd_one.mpr <|
+      hp.coeff_natDegree ▸ (C_dvd_iff_dvd_coeff _ _).mp h p.natDegree,
+   fun ha => (ha.map C).dvd⟩
+
+theorem degree_pos_of_not_isUnit_of_dvd_monic {a p : R[X]} (ha : ¬ IsUnit a)
+    (hap : a ∣ p) (hp : Monic p) :
+    0 < degree a :=
+  lt_of_not_ge <| fun h => ha <| by
+    rw [Polynomial.eq_C_of_degree_le_zero h] at hap ⊢
+    simpa [hp.C_dvd_iff_isUnit, isUnit_C] using hap
+
+theorem natDegree_pos_of_not_isUnit_of_dvd_monic {a p : R[X]} (ha : ¬ IsUnit a)
+    (hap : a ∣ p) (hp : Monic p) :
+    0 < natDegree a :=
+  natDegree_pos_iff_degree_pos.mpr <| degree_pos_of_not_isUnit_of_dvd_monic ha hap hp
+
+theorem degree_pos_of_monic_of_not_isUnit {a : R[X]} (hu : ¬ IsUnit a) (ha : Monic a) :
+    0 < degree a :=
+  degree_pos_of_not_isUnit_of_dvd_monic hu dvd_rfl ha
+
+theorem natDegree_pos_of_monic_of_not_isUnit {a : R[X]} (hu : ¬ IsUnit a) (ha : Monic a) :
+    0 < natDegree a :=
+  natDegree_pos_iff_degree_pos.mpr <| degree_pos_of_monic_of_not_isUnit hu ha
+
+end CommSemiring
+
 section CommRing
 
 variable [CommRing R]
@@ -1440,6 +1494,31 @@ theorem prod_multiset_X_sub_C_of_monic_of_roots_card_eq (hp : p.Monic)
 set_option linter.uppercaseLean3 false in
 #align polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq Polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq
 
+theorem Monic.isUnit_leadingCoeff_of_dvd {a p : R[X]} (hp : Monic p) (hap : a ∣ p) :
+    IsUnit a.leadingCoeff :=
+  isUnit_of_dvd_one (by simpa only [hp.leadingCoeff] using leadingCoeff_dvd_leadingCoeff hap)
+
+/-- To check a monic polynomial is irreducible, it suffices to check only for
+divisors that have smaller degree.
+
+See also: `Polynomial.Monic.irreducible_iff_natDegree`.
+-/
+theorem Monic.irreducible_iff_degree_lt {p : R[X]} (p_monic : Monic p) (p_1 : p ≠ 1) :
+    Irreducible p ↔ ∀ q, degree q ≤ ↑(p.natDegree / 2) → q ∣ p → IsUnit q := by
+  simp only [p_monic.irreducible_iff_lt_natDegree_lt p_1, mem_Ioc, and_imp,
+    natDegree_pos_iff_degree_pos, natDegree_le_iff_degree_le]
+  constructor
+  · rintro h q deg_le dvd
+    by_contra q_unit
+    have := degree_pos_of_not_isUnit_of_dvd_monic q_unit dvd p_monic
+    have hu := p_monic.isUnit_leadingCoeff_of_dvd dvd
+    refine (h _ (monic_of_isUnit_leadingCoeff_inv_smul hu) ?_ ?_ (dvd_trans ?_ dvd)).elim
+    · rwa [degree_smul_of_smul_regular _ (isSMulRegular_of_group _)]
+    · rwa [degree_smul_of_smul_regular _ (isSMulRegular_of_group _)]
+    · rw [Units.smul_def, Polynomial.smul_eq_C_mul, (isUnit_C.mpr (Units.isUnit _)).mul_left_dvd]
+  · rintro h q _ deg_pos deg_le dvd
+    exact deg_pos.ne' <| degree_eq_zero_of_isUnit (h q deg_le dvd)
+
 end CommRing
 
 section

This cleans up instances of

⟨ foo, bar⟩

and

⟨foo, bar ⟩

where spaces a on the inside one side, but not on the other side. Fixing this by removing the extra space.

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

@@ -329,7 +329,7 @@ theorem Monic.not_irreducible_iff_exists_add_mul_eq_coeff (hm : p.Monic) (hnd :
     simpa only [nextCoeff, hnd, add_right_cancel hda, hdb] using ha.nextCoeff_mul hb
   · rintro ⟨c₁, c₂, hmul, hadd⟩
     refine
-      ⟨X + C c₁, X + C c₂, monic_X_add_C _, monic_X_add_C _, ?_, ?_ ⟩
+      ⟨X + C c₁, X + C c₂, monic_X_add_C _, monic_X_add_C _, ?_, ?_⟩
     · rw [p.as_sum_range_C_mul_X_pow, hnd, Finset.sum_range_succ, Finset.sum_range_succ,
         Finset.sum_range_one, ← hnd, hm.coeff_natDegree, hnd, hmul, hadd, C_mul, C_add, C_1]
       ring

@@ -1339,6 +1339,16 @@ lemma eq_zero_of_natDegree_lt_card_of_eval_eq_zero' {R} [CommRing R] [IsDomain R
   eq_zero_of_natDegree_lt_card_of_eval_eq_zero p Subtype.val_injective
     (fun i : s ↦ heval i i.prop) (hcard.trans_eq (Fintype.card_coe s).symm)
 
+open Cardinal in
+lemma exists_eval_ne_zero_of_natDegree_lt_card (f : R[X]) (hf : f ≠ 0) (hfR : f.natDegree < #R) :
+    ∃ r, f.eval r ≠ 0 := by
+  contrapose! hf
+  obtain hR|hR := finite_or_infinite R
+  · have := Fintype.ofFinite R
+    apply eq_zero_of_natDegree_lt_card_of_eval_eq_zero f Function.injective_id hf
+    aesop
+  · exact zero_of_eval_zero _ hf
+
 theorem isCoprime_X_sub_C_of_isUnit_sub {R} [CommRing R] {a b : R} (h : IsUnit (a - b)) :
     IsCoprime (X - C a) (X - C b) :=
   ⟨-C h.unit⁻¹.val, C h.unit⁻¹.val, by

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>

@@ -596,7 +596,7 @@ theorem exists_multiset_roots [DecidableEq R] :
       ⟨0, (degree_eq_natDegree hp).symm ▸ WithBot.coe_le_coe.2 (Nat.zero_le _), by
         intro a
         rw [count_zero, rootMultiplicity_eq_zero (not_exists.mp h a)]⟩
-termination_by _ p _ => natDegree p
+termination_by p => natDegree p
 decreasing_by {
   simp_wf
   apply (Nat.cast_lt (α := WithBot ℕ)).mp

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

From LeanAPAP

@@ -155,12 +155,10 @@ theorem trailingDegree_mul : (p * q).trailingDegree = p.trailingDegree + q.trail
 @[simp]
 theorem natDegree_pow (p : R[X]) (n : ℕ) : natDegree (p ^ n) = n * natDegree p := by
   classical
-  exact if hp0 : p = 0 then
-    if hn0 : n = 0 then by simp [hp0, hn0]
-    else by rw [hp0, zero_pow (Nat.pos_of_ne_zero hn0)]; simp
-  else
-    natDegree_pow'
-      (by rw [← leadingCoeff_pow, Ne.def, leadingCoeff_eq_zero]; exact pow_ne_zero _ hp0)
+  obtain rfl | hp := eq_or_ne p 0
+  · obtain rfl | hn := eq_or_ne n 0 <;> simp [*]
+  exact natDegree_pow' $ by
+    rw [← leadingCoeff_pow, Ne.def, leadingCoeff_eq_zero]; exact pow_ne_zero _ hp
 #align polynomial.nat_degree_pow Polynomial.natDegree_pow
 
 theorem degree_le_mul_left (p : R[X]) (hq : q ≠ 0) : degree p ≤ degree (p * q) := by
@@ -811,7 +809,7 @@ theorem roots_pow (p : R[X]) (n : ℕ) : (p ^ n).roots = n • p.roots := by
   induction' n with n ihn
   · rw [pow_zero, roots_one, Nat.zero_eq, zero_smul, empty_eq_zero]
   · rcases eq_or_ne p 0 with (rfl | hp)
-    · rw [zero_pow n.succ_pos, roots_zero, smul_zero]
+    · rw [zero_pow n.succ_ne_zero, roots_zero, smul_zero]
     · rw [pow_succ', roots_mul (mul_ne_zero (pow_ne_zero _ hp) hp), ihn, Nat.succ_eq_add_one,
         add_smul, one_smul]
 #align polynomial.roots_pow Polynomial.roots_pow
@@ -957,7 +955,7 @@ theorem ne_zero_of_mem_nthRootsFinset {η : R} (hη : η ∈ nthRootsFinset n R)
   | zero =>
     simp only [Nat.zero_eq, nthRootsFinset_zero, not_mem_empty] at hη
   | succ n =>
-    rw [mem_nthRootsFinset n.succ_pos, zero_pow n.succ_pos] at hη
+    rw [mem_nthRootsFinset n.succ_pos, zero_pow n.succ_ne_zero] at hη
     exact zero_ne_one hη
 
 theorem one_mem_nthRootsFinset (hn : 0 < n) : 1 ∈ nthRootsFinset n R := by

• Add WithBot.lt_coe_bot and WithTop.coe_top_lt.
• Use them to golf Nat.WithBot.lt_zero_iff, make n argument implicit.
• Add section Preorder for WithBot and WithTop.
• Move some lemmas to appropriate sections.
• Add simp to WithBot.bot_lt_coe and WithTop.coe_lt_top.
• Use the OrderDual trick to golf some proofs.

@@ -1257,7 +1257,7 @@ theorem leadingCoeff_divByMonic_X_sub_C (p : R[X]) (hp : degree p ≠ 0) (a : R)
     leadingCoeff (p /ₘ (X - C a)) = leadingCoeff p := by
   nontriviality
   cases' hp.lt_or_lt with hd hd
-  · rw [degree_eq_bot.mp <| (Nat.WithBot.lt_zero_iff _).mp hd, zero_divByMonic]
+  · rw [degree_eq_bot.mp <| Nat.WithBot.lt_zero_iff.mp hd, zero_divByMonic]
   refine' leadingCoeff_divByMonic_of_monic (monic_X_sub_C a) _
   rwa [degree_X_sub_C, Nat.WithBot.one_le_iff_zero_lt]
 set_option linter.uppercaseLean3 false in

@@ -1072,8 +1072,8 @@ theorem aroots_one [CommRing S] [IsDomain S] [Algebra T S] :
 
 @[simp]
 theorem aroots_neg [CommRing S] [IsDomain S] [Algebra T S] (p : T[X]) :
-    (-p).aroots S = p.aroots S :=
-  by rw [aroots, Polynomial.map_neg, roots_neg]
+    (-p).aroots S = p.aroots S := by
+  rw [aroots, Polynomial.map_neg, roots_neg]
 
 @[simp]
 theorem aroots_C_mul [CommRing S] [IsDomain S] [Algebra T S]

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -3,7 +3,6 @@ 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, Johan Commelin
 -/
-import Mathlib.Algebra.CharZero.Infinite
 import Mathlib.Data.Polynomial.AlgebraMap
 import Mathlib.Data.Polynomial.Degree.Lemmas
 import Mathlib.Data.Polynomial.Div

See Zulip thread for the discussion.

@@ -15,7 +15,7 @@ import Mathlib.Algebra.Polynomial.BigOperators
 /-!
 # Theory of univariate polynomials
 
-This file starts looking like the ring theory of $ R[X] $
+This file starts looking like the ring theory of $R[X]$
 
 ## Main definitions
 

Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>

@@ -1264,6 +1264,37 @@ theorem leadingCoeff_divByMonic_X_sub_C (p : R[X]) (hp : degree p ≠ 0) (a : R)
 set_option linter.uppercaseLean3 false in
 #align polynomial.leading_coeff_div_by_monic_X_sub_C Polynomial.leadingCoeff_divByMonic_X_sub_C
 
+theorem eq_of_dvd_of_natDegree_le_of_leadingCoeff {p q : R[X]} (hpq : p ∣ q)
+    (h₁ : q.natDegree ≤ p.natDegree) (h₂ : p.leadingCoeff = q.leadingCoeff) :
+    p = q := by
+  by_cases hq : q = 0
+  · rwa [hq, leadingCoeff_zero, leadingCoeff_eq_zero, ← hq] at h₂
+  replace h₁ := (natDegree_le_of_dvd hpq hq).antisymm h₁
+  obtain ⟨u, rfl⟩ := hpq
+  replace hq := mul_ne_zero_iff.mp hq
+  rw [natDegree_mul hq.1 hq.2, self_eq_add_right] at h₁
+  rw [eq_C_of_natDegree_eq_zero h₁, leadingCoeff_mul, leadingCoeff_C,
+    eq_comm, mul_eq_left₀ (leadingCoeff_ne_zero.mpr hq.1)] at h₂
+  rw [eq_C_of_natDegree_eq_zero h₁, h₂, map_one, mul_one]
+
+theorem associated_of_dvd_of_natDegree_le_of_leadingCoeff {p q : R[X]} (hpq : p ∣ q)
+    (h₁ : q.natDegree ≤ p.natDegree) (h₂ : q.leadingCoeff ∣ p.leadingCoeff) :
+    Associated p q :=
+  have ⟨r, hr⟩ := hpq
+  have ⟨u, hu⟩ := associated_of_dvd_dvd ⟨leadingCoeff r, hr ▸ leadingCoeff_mul p r⟩ h₂
+  ⟨Units.map C.toMonoidHom u, eq_of_dvd_of_natDegree_le_of_leadingCoeff
+    (by rwa [Units.mul_right_dvd]) (by simpa [natDegree_mul_C] using h₁) (by simpa using hu)⟩
+
+theorem associated_of_dvd_of_natDegree_le {K} [Field K] {p q : K[X]} (hpq : p ∣ q) (hq : q ≠ 0)
+    (h₁ : q.natDegree ≤ p.natDegree) : Associated p q :=
+  associated_of_dvd_of_natDegree_le_of_leadingCoeff hpq h₁
+    (IsUnit.dvd (by rwa [← leadingCoeff_ne_zero, ← isUnit_iff_ne_zero] at hq))
+
+theorem associated_of_dvd_of_degree_eq {K} [Field K] {p q : K[X]} (hpq : p ∣ q)
+    (h₁ : p.degree = q.degree) : Associated p q :=
+  (Classical.em (q = 0)).elim (fun hq ↦ (show p = q by simpa [hq] using h₁) ▸ Associated.refl p)
+    (associated_of_dvd_of_natDegree_le hpq · (natDegree_le_natDegree h₁.ge))
+
 theorem eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le {R} [CommRing R] {p q : R[X]}
     (hp : p.Monic) (hdiv : p ∣ q) (hdeg : q.natDegree ≤ p.natDegree) :
     q = C q.leadingCoeff * p := by

Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>

@@ -890,6 +890,11 @@ theorem nthRoots_zero (r : R) : nthRoots 0 r = 0 := by
   simp only [empty_eq_zero, pow_zero, nthRoots, ← C_1, ← C_sub, roots_C]
 #align polynomial.nth_roots_zero Polynomial.nthRoots_zero
 
+@[simp]
+theorem nthRoots_zero_right {R} [CommRing R] [IsDomain R] (n : ℕ) :
+    nthRoots n (0 : R) = Multiset.replicate n 0 := by
+  rw [nthRoots, C.map_zero, sub_zero, roots_pow, roots_X, Multiset.nsmul_singleton]
+
 theorem card_nthRoots (n : ℕ) (a : R) : Multiset.card (nthRoots n a) ≤ n := by
   classical exact
   (if hn : n = 0 then

Change a few lemma names that have historically bothered me.

• Finset.card_le_of_subset → Finset.card_le_card
• Multiset.card_le_of_le → Multiset.card_le_card
• Multiset.card_lt_of_lt → Multiset.card_lt_card
• Set.ncard_le_of_subset → Set.ncard_le_ncard
• Finset.image_filter → Finset.filter_image
• CompleteLattice.finset_sup_compact_of_compact → CompleteLattice.isCompactElement_finset_sup

@@ -693,7 +693,7 @@ lemma mem_roots_iff_aeval_eq_zero (w : p ≠ 0) : x ∈ roots p ↔ aeval x p =
 
 theorem card_le_degree_of_subset_roots {p : R[X]} {Z : Finset R} (h : Z.val ⊆ p.roots) :
     Z.card ≤ p.natDegree :=
-  (Multiset.card_le_of_le (Finset.val_le_iff_val_subset.2 h)).trans (Polynomial.card_roots' p)
+  (Multiset.card_le_card (Finset.val_le_iff_val_subset.2 h)).trans (Polynomial.card_roots' p)
 #align polynomial.card_le_degree_of_subset_roots Polynomial.card_le_degree_of_subset_roots
 
 theorem finite_setOf_isRoot {p : R[X]} (hp : p ≠ 0) : Set.Finite { x | IsRoot p x } := by
@@ -1460,7 +1460,7 @@ theorem map_roots_le_of_injective [IsDomain A] [IsDomain B] (p : A[X]) {f : A 
 theorem card_roots_le_map [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (h : p.map f ≠ 0) :
     Multiset.card p.roots ≤ Multiset.card (p.map f).roots := by
   rw [← p.roots.card_map f]
-  exact Multiset.card_le_of_le (map_roots_le h)
+  exact Multiset.card_le_card (map_roots_le h)
 #align polynomial.card_roots_le_map Polynomial.card_roots_le_map
 
 theorem card_roots_le_map_of_injective [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B}

This PR adds negation lemmas for roots, aroots, and rootSet.

@@ -784,6 +784,10 @@ theorem roots_smul_nonzero (p : R[X]) (ha : a ≠ 0) : (a • p).roots = p.roots
   rw [smul_eq_C_mul, roots_C_mul _ ha]
 #align polynomial.roots_smul_nonzero Polynomial.roots_smul_nonzero
 
+@[simp]
+lemma roots_neg (p : R[X]) : (-p).roots = p.roots := by
+  rw [← neg_one_smul R p, roots_smul_nonzero p (neg_ne_zero.mpr one_ne_zero)]
+
 theorem roots_list_prod (L : List R[X]) :
     (0 : R[X]) ∉ L → L.prod.roots = (L : Multiset R[X]).bind roots :=
   List.recOn L (fun _ => roots_one) fun hd tl ih H => by
@@ -1062,6 +1066,11 @@ theorem aroots_one [CommRing S] [IsDomain S] [Algebra T S] :
     (1 : T[X]).aroots S = 0 :=
   aroots_C 1
 
+@[simp]
+theorem aroots_neg [CommRing S] [IsDomain S] [Algebra T S] (p : T[X]) :
+    (-p).aroots S = p.aroots S :=
+  by rw [aroots, Polynomial.map_neg, roots_neg]
+
 @[simp]
 theorem aroots_C_mul [CommRing S] [IsDomain S] [Algebra T S]
     [NoZeroSMulDivisors T S] {a : T} (p : T[X]) (ha : a ≠ 0) :
@@ -1123,6 +1132,15 @@ theorem rootSet_zero (S) [CommRing S] [IsDomain S] [Algebra T S] : (0 : T[X]).ro
   rw [← C_0, rootSet_C]
 #align polynomial.root_set_zero Polynomial.rootSet_zero
 
+@[simp]
+theorem rootSet_one (S) [CommRing S] [IsDomain S] [Algebra T S] : (1 : T[X]).rootSet S = ∅ := by
+  rw [← C_1, rootSet_C]
+
+@[simp]
+theorem rootSet_neg (p : T[X]) (S) [CommRing S] [IsDomain S] [Algebra T S] :
+    (-p).rootSet S = p.rootSet S := by
+  rw [rootSet, aroots_neg, rootSet]
+
 instance rootSetFintype (p : T[X]) (S : Type*) [CommRing S] [IsDomain S] [Algebra T S] :
     Fintype (p.rootSet S) :=
   FinsetCoe.fintype _

Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>

@@ -1263,6 +1263,31 @@ theorem eq_of_monic_of_dvd_of_natDegree_le {R} [CommRing R] {p q : R[X]} (hp : p
   rw [hq.leadingCoeff, C_1, one_mul]
 #align polynomial.eq_of_monic_of_dvd_of_nat_degree_le Polynomial.eq_of_monic_of_dvd_of_natDegree_le
 
+lemma eq_zero_of_natDegree_lt_card_of_eval_eq_zero {R} [CommRing R] [IsDomain R]
+    (p : R[X]) {ι} [Fintype ι] {f : ι → R} (hf : Function.Injective f)
+    (heval : ∀ i, p.eval (f i) = 0) (hcard : natDegree p < Fintype.card ι) : p = 0 := by
+  classical
+  by_contra hp
+  apply not_lt_of_le (le_refl (Finset.card p.roots.toFinset))
+  calc
+    Finset.card p.roots.toFinset ≤ Multiset.card p.roots := Multiset.toFinset_card_le _
+    _ ≤ natDegree p := Polynomial.card_roots' p
+    _ < Fintype.card ι := hcard
+    _ = Fintype.card (Set.range f) := (Set.card_range_of_injective hf).symm
+    _ = Finset.card (Finset.univ.image f) := by rw [← Set.toFinset_card, Set.toFinset_range]
+    _ ≤ Finset.card p.roots.toFinset := Finset.card_mono ?_
+  intro _
+  simp only [Finset.mem_image, Finset.mem_univ, true_and, Multiset.mem_toFinset, mem_roots', ne_eq,
+    IsRoot.def, forall_exists_index, hp, not_false_eq_true]
+  rintro x rfl
+  exact heval _
+
+lemma eq_zero_of_natDegree_lt_card_of_eval_eq_zero' {R} [CommRing R] [IsDomain R]
+    (p : R[X]) (s : Finset R) (heval : ∀ i ∈ s, p.eval i = 0) (hcard : natDegree p < s.card) :
+    p = 0 :=
+  eq_zero_of_natDegree_lt_card_of_eval_eq_zero p Subtype.val_injective
+    (fun i : s ↦ heval i i.prop) (hcard.trans_eq (Fintype.card_coe s).symm)
+
 theorem isCoprime_X_sub_C_of_isUnit_sub {R} [CommRing R] {a b : R} (h : IsUnit (a - b)) :
     IsCoprime (X - C a) (X - C b) :=
   ⟨-C h.unit⁻¹.val, C h.unit⁻¹.val, by

Main changes:

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

In Data/Polynomial/FieldDivision:

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

In addition:

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

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

@@ -394,15 +394,123 @@ theorem pow_rootMultiplicity_not_dvd {p : R[X]} (p0 : p ≠ 0) (a : R) :
     ¬(X - C a) ^ (rootMultiplicity a p + 1) ∣ p := by rw [← rootMultiplicity_le_iff p0]
 #align polynomial.pow_root_multiplicity_not_dvd Polynomial.pow_rootMultiplicity_not_dvd
 
+theorem X_sub_C_pow_dvd_iff {p : R[X]} {t : R} {n : ℕ} :
+    (X - C t) ^ n ∣ p ↔ X ^ n ∣ p.comp (X + C t) := by
+  convert (map_dvd_iff <| algEquivAevalXAddC t).symm using 2
+  simp [C_eq_algebraMap]
+
+theorem comp_X_add_C_eq_zero_iff {p : R[X]} (t : R) :
+    p.comp (X + C t) = 0 ↔ p = 0 := AddEquivClass.map_eq_zero_iff (algEquivAevalXAddC t)
+
+theorem comp_X_add_C_ne_zero_iff {p : R[X]} (t : R) :
+    p.comp (X + C t) ≠ 0 ↔ p ≠ 0 := Iff.not <| comp_X_add_C_eq_zero_iff t
+
+theorem rootMultiplicity_eq_rootMultiplicity {p : R[X]} {t : R} :
+    p.rootMultiplicity t = (p.comp (X + C t)).rootMultiplicity 0 := by
+  classical
+  simp_rw [rootMultiplicity_eq_multiplicity, comp_X_add_C_eq_zero_iff]
+  congr; ext; congr 1
+  rw [C_0, sub_zero]
+  convert (multiplicity.multiplicity_map_eq <| algEquivAevalXAddC t).symm using 2
+  simp [C_eq_algebraMap]
+
+theorem rootMultiplicity_eq_natTrailingDegree' {p : R[X]} :
+    p.rootMultiplicity 0 = p.natTrailingDegree := by
+  by_cases h : p = 0
+  · simp only [h, rootMultiplicity_zero, natTrailingDegree_zero]
+  refine le_antisymm ?_ ?_
+  · rw [rootMultiplicity_le_iff h, map_zero, sub_zero, X_pow_dvd_iff, not_forall]
+    exact ⟨p.natTrailingDegree,
+      fun h' ↦ trailingCoeff_nonzero_iff_nonzero.2 h <| h' <| Nat.lt.base _⟩
+  · rw [le_rootMultiplicity_iff h, map_zero, sub_zero, X_pow_dvd_iff]
+    exact fun _ ↦ coeff_eq_zero_of_lt_natTrailingDegree
+
+theorem rootMultiplicity_eq_natTrailingDegree {p : R[X]} {t : R} :
+    p.rootMultiplicity t = (p.comp (X + C t)).natTrailingDegree :=
+  rootMultiplicity_eq_rootMultiplicity.trans rootMultiplicity_eq_natTrailingDegree'
+
+theorem eval_divByMonic_eq_trailingCoeff_comp {p : R[X]} {t : R} :
+    (p /ₘ (X - C t) ^ p.rootMultiplicity t).eval t = (p.comp (X + C t)).trailingCoeff := by
+  obtain rfl | hp := eq_or_ne p 0
+  · rw [zero_divByMonic, eval_zero, zero_comp, trailingCoeff_zero]
+  have mul_eq := p.pow_mul_divByMonic_rootMultiplicity_eq t
+  set m := p.rootMultiplicity t
+  set g := p /ₘ (X - C t) ^ m
+  have : (g.comp (X + C t)).coeff 0 = g.eval t
+  · rw [coeff_zero_eq_eval_zero, eval_comp, eval_add, eval_X, eval_C, zero_add]
+  rw [← congr_arg (comp · <| X + C t) mul_eq, mul_comp, pow_comp, sub_comp, X_comp, C_comp,
+    add_sub_cancel, ← reverse_leadingCoeff, reverse_X_pow_mul, reverse_leadingCoeff, trailingCoeff,
+    Nat.le_zero.mp (natTrailingDegree_le_of_ne_zero <|
+      this ▸ eval_divByMonic_pow_rootMultiplicity_ne_zero t hp), this]
+
+section nonZeroDivisors
+
+open scoped nonZeroDivisors
+
+theorem Monic.mem_nonZeroDivisors {p : R[X]} (h : p.Monic) : p ∈ R[X]⁰ :=
+  mem_nonZeroDivisors_iff.2 fun _ hx ↦ (mul_left_eq_zero_iff h).1 hx
+
+theorem mem_nonZeroDivisors_of_leadingCoeff {p : R[X]} (h : p.leadingCoeff ∈ R⁰) : p ∈ R[X]⁰ := by
+  refine mem_nonZeroDivisors_iff.2 fun x hx ↦ leadingCoeff_eq_zero.1 ?_
+  by_contra hx'
+  rw [← mul_right_mem_nonZeroDivisors_eq_zero_iff h] at hx'
+  simp only [← leadingCoeff_mul' hx', hx, leadingCoeff_zero, not_true] at hx'
+
+end nonZeroDivisors
+
+theorem rootMultiplicity_mul_X_sub_C_pow {p : R[X]} {a : R} {n : ℕ} (h : p ≠ 0) :
+    (p * (X - C a) ^ n).rootMultiplicity a = p.rootMultiplicity a + n := by
+  have h2 := monic_X_sub_C a |>.pow n |>.mul_left_ne_zero h
+  refine le_antisymm ?_ ?_
+  · rw [rootMultiplicity_le_iff h2, add_assoc, add_comm n, ← add_assoc, pow_add,
+      dvd_cancel_right_mem_nonZeroDivisors (monic_X_sub_C a |>.pow n |>.mem_nonZeroDivisors)]
+    exact pow_rootMultiplicity_not_dvd h a
+  · rw [le_rootMultiplicity_iff h2, pow_add]
+    exact mul_dvd_mul_right (pow_rootMultiplicity_dvd p a) _
+
+/-- The multiplicity of `a` as root of `(X - a) ^ n` is `n`. -/
+theorem rootMultiplicity_X_sub_C_pow [Nontrivial R] (a : R) (n : ℕ) :
+    rootMultiplicity a ((X - C a) ^ n) = n := by
+  have := rootMultiplicity_mul_X_sub_C_pow (a := a) (n := n) C.map_one_ne_zero
+  rwa [rootMultiplicity_C, map_one, one_mul, zero_add] at this
+set_option linter.uppercaseLean3 false in
+#align polynomial.root_multiplicity_X_sub_C_pow Polynomial.rootMultiplicity_X_sub_C_pow
+
+theorem rootMultiplicity_X_sub_C_self [Nontrivial R] {x : R} :
+    rootMultiplicity x (X - C x) = 1 :=
+  pow_one (X - C x) ▸ rootMultiplicity_X_sub_C_pow x 1
+set_option linter.uppercaseLean3 false in
+#align polynomial.root_multiplicity_X_sub_C_self Polynomial.rootMultiplicity_X_sub_C_self
+
+-- porting note: swapped instance argument order
+theorem rootMultiplicity_X_sub_C [Nontrivial R] [DecidableEq R] {x y : R} :
+    rootMultiplicity x (X - C y) = if x = y then 1 else 0 := by
+  split_ifs with hxy
+  · rw [hxy]
+    exact rootMultiplicity_X_sub_C_self
+  exact rootMultiplicity_eq_zero (mt root_X_sub_C.mp (Ne.symm hxy))
+set_option linter.uppercaseLean3 false in
+#align polynomial.root_multiplicity_X_sub_C Polynomial.rootMultiplicity_X_sub_C
+
 /-- The multiplicity of `p + q` is at least the minimum of the multiplicities. -/
 theorem rootMultiplicity_add {p q : R[X]} (a : R) (hzero : p + q ≠ 0) :
     min (rootMultiplicity a p) (rootMultiplicity a q) ≤ rootMultiplicity a (p + q) := by
   rw [le_rootMultiplicity_iff hzero]
-  have hdivp : (X - C a) ^ rootMultiplicity a p ∣ p := pow_rootMultiplicity_dvd p a
-  have hdivq : (X - C a) ^ rootMultiplicity a q ∣ q := pow_rootMultiplicity_dvd q a
-  exact min_pow_dvd_add hdivp hdivq
+  exact min_pow_dvd_add (pow_rootMultiplicity_dvd p a) (pow_rootMultiplicity_dvd q a)
 #align polynomial.root_multiplicity_add Polynomial.rootMultiplicity_add
 
+theorem le_rootMultiplicity_mul {p q : R[X]} (x : R) (hpq : p * q ≠ 0) :
+    rootMultiplicity x p + rootMultiplicity x q ≤ rootMultiplicity x (p * q) := by
+  rw [le_rootMultiplicity_iff hpq, pow_add]
+  exact mul_dvd_mul (pow_rootMultiplicity_dvd p x) (pow_rootMultiplicity_dvd q x)
+
+theorem rootMultiplicity_mul' {p q : R[X]} {x : R}
+    (hpq : (p /ₘ (X - C x) ^ p.rootMultiplicity x).eval x *
+      (q /ₘ (X - C x) ^ q.rootMultiplicity x).eval x ≠ 0) :
+    rootMultiplicity x (p * q) = rootMultiplicity x p + rootMultiplicity x q := by
+  simp_rw [eval_divByMonic_eq_trailingCoeff_comp] at hpq
+  simp_rw [rootMultiplicity_eq_natTrailingDegree, mul_comp, natTrailingDegree_mul' hpq]
+
 variable [IsDomain R] {p q : R[X]}
 
 section Roots
@@ -441,14 +549,6 @@ theorem Monic.irreducible_of_degree_eq_one (hp1 : degree p = 1) (hm : Monic p) :
   (hm.prime_of_degree_eq_one hp1).irreducible
 #align polynomial.monic.irreducible_of_degree_eq_one Polynomial.Monic.irreducible_of_degree_eq_one
 
-theorem eq_of_monic_of_associated (hp : p.Monic) (hq : q.Monic) (hpq : Associated p q) : p = q := by
-  obtain ⟨u, hu⟩ := hpq
-  unfold Monic at hp hq
-  rw [eq_C_of_degree_le_zero (degree_coe_units _).le] at hu
-  rw [← hu, leadingCoeff_mul, hp, one_mul, leadingCoeff_C] at hq
-  rwa [hq, C_1, mul_one] at hu
-#align polynomial.eq_of_monic_of_associated Polynomial.eq_of_monic_of_associated
-
 theorem rootMultiplicity_mul {p q : R[X]} {x : R} (hpq : p * q ≠ 0) :
     rootMultiplicity x (p * q) = rootMultiplicity x p + rootMultiplicity x q := by
   classical
@@ -459,34 +559,6 @@ theorem rootMultiplicity_mul {p q : R[X]} {x : R} (hpq : p * q ≠ 0) :
     multiplicity.mul' (prime_X_sub_C x)]
 #align polynomial.root_multiplicity_mul Polynomial.rootMultiplicity_mul
 
-theorem rootMultiplicity_X_sub_C_self {x : R} : rootMultiplicity x (X - C x) = 1 := by
-  classical
-  rw [rootMultiplicity_eq_multiplicity, dif_neg (X_sub_C_ne_zero x),
-    multiplicity.get_multiplicity_self]
-set_option linter.uppercaseLean3 false in
-#align polynomial.root_multiplicity_X_sub_C_self Polynomial.rootMultiplicity_X_sub_C_self
-
--- porting note: swapped instance argument order
-theorem rootMultiplicity_X_sub_C [DecidableEq R] {x y : R} :
-    rootMultiplicity x (X - C y) = if x = y then 1 else 0 := by
-  split_ifs with hxy
-  · rw [hxy]
-    exact rootMultiplicity_X_sub_C_self
-  exact rootMultiplicity_eq_zero (mt root_X_sub_C.mp (Ne.symm hxy))
-set_option linter.uppercaseLean3 false in
-#align polynomial.root_multiplicity_X_sub_C Polynomial.rootMultiplicity_X_sub_C
-
-/-- The multiplicity of `a` as root of `(X - a) ^ n` is `n`. -/
-theorem rootMultiplicity_X_sub_C_pow (a : R) (n : ℕ) : rootMultiplicity a ((X - C a) ^ n) = n := by
-  induction' n with n hn
-  · refine' rootMultiplicity_eq_zero _
-    simp only [eval_one, IsRoot.def, not_false_iff, one_ne_zero, pow_zero, Nat.zero_eq]
-  have hzero := pow_ne_zero n.succ (X_sub_C_ne_zero a)
-  rw [pow_succ (X - C a) n] at hzero ⊢
-  simp only [rootMultiplicity_mul hzero, rootMultiplicity_X_sub_C_self, hn, Nat.one_add]
-set_option linter.uppercaseLean3 false in
-#align polynomial.root_multiplicity_X_sub_C_pow Polynomial.rootMultiplicity_X_sub_C_pow
-
 theorem exists_multiset_roots [DecidableEq R] :
     ∀ {p : R[X]} (_ : p ≠ 0), ∃ s : Multiset R,
       (Multiset.card s : WithBot ℕ) ≤ degree p ∧ ∀ a, s.count a = rootMultiplicity a p

@@ -1338,7 +1338,7 @@ theorem map_roots_le [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (h : p
 theorem map_roots_le_of_injective [IsDomain A] [IsDomain B] (p : A[X]) {f : A →+* B}
     (hf : Function.Injective f) : p.roots.map f ≤ (p.map f).roots := by
   by_cases hp0 : p = 0
-  · simp only [hp0, roots_zero, Multiset.map_zero, Polynomial.map_zero]; rfl
+  · simp only [hp0, roots_zero, Multiset.map_zero, Polynomial.map_zero, le_rfl]
   exact map_roots_le ((Polynomial.map_ne_zero_iff hf).mpr hp0)
 #align polynomial.map_roots_le_of_injective Polynomial.map_roots_le_of_injective
 
@@ -1351,7 +1351,7 @@ theorem card_roots_le_map [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (
 theorem card_roots_le_map_of_injective [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B}
     (hf : Function.Injective f) : Multiset.card p.roots ≤ Multiset.card (p.map f).roots := by
   by_cases hp0 : p = 0
-  · simp only [hp0, roots_zero, Polynomial.map_zero, Multiset.card_zero]; rfl
+  · simp only [hp0, roots_zero, Polynomial.map_zero, Multiset.card_zero, le_rfl]
   exact card_roots_le_map ((Polynomial.map_ne_zero_iff hf).mpr hp0)
 #align polynomial.card_roots_le_map_of_injective Polynomial.card_roots_le_map_of_injective
 

From flt-regular.

Co-authored-by: Andrew Yang <the.erd.one@gmail.com>

@@ -860,6 +860,29 @@ theorem mem_nthRootsFinset {n : ℕ} (h : 0 < n) {x : R} :
 theorem nthRootsFinset_zero : nthRootsFinset 0 R = ∅ := by classical simp [nthRootsFinset_def]
 #align polynomial.nth_roots_finset_zero Polynomial.nthRootsFinset_zero
 
+theorem mul_mem_nthRootsFinset
+    {η₁ η₂ : R} (hη₁ : η₁ ∈ nthRootsFinset n R) (hη₂ : η₂ ∈ nthRootsFinset n R) :
+    η₁ * η₂ ∈ nthRootsFinset n R := by
+  cases n with
+  | zero =>
+    simp only [Nat.zero_eq, nthRootsFinset_zero, not_mem_empty] at hη₁
+  | succ n =>
+    rw [mem_nthRootsFinset n.succ_pos] at hη₁ hη₂ ⊢
+    rw [mul_pow, hη₁, hη₂, one_mul]
+
+theorem ne_zero_of_mem_nthRootsFinset {η : R} (hη : η ∈ nthRootsFinset n R) : η ≠ 0 := by
+  nontriviality R
+  rintro rfl
+  cases n with
+  | zero =>
+    simp only [Nat.zero_eq, nthRootsFinset_zero, not_mem_empty] at hη
+  | succ n =>
+    rw [mem_nthRootsFinset n.succ_pos, zero_pow n.succ_pos] at hη
+    exact zero_ne_one hη
+
+theorem one_mem_nthRootsFinset (hn : 0 < n) : 1 ∈ nthRootsFinset n R := by
+  rw [mem_nthRootsFinset hn, one_pow]
+
 end NthRoots
 
 theorem Monic.comp (hp : p.Monic) (hq : q.Monic) (h : q.natDegree ≠ 0) : (p.comp q).Monic := by

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

@@ -139,8 +139,8 @@ instance : NoZeroDivisors R[X] where
     rw [← leadingCoeff_zero, ← leadingCoeff_mul, h]
 
 theorem natDegree_mul (hp : p ≠ 0) (hq : q ≠ 0) : (p*q).natDegree = p.natDegree + q.natDegree := by
-  rw [← Nat.cast_inj (R := WithBot ℕ), ←degree_eq_natDegree (mul_ne_zero hp hq),
-    Nat.cast_add,  ←degree_eq_natDegree hp, ← degree_eq_natDegree hq, degree_mul]
+  rw [← Nat.cast_inj (R := WithBot ℕ), ← degree_eq_natDegree (mul_ne_zero hp hq),
+    Nat.cast_add, ← degree_eq_natDegree hp, ← degree_eq_natDegree hq, degree_mul]
 #align polynomial.nat_degree_mul Polynomial.natDegree_mul
 
 theorem trailingDegree_mul : (p * q).trailingDegree = p.trailingDegree + q.trailingDegree := by
@@ -1172,7 +1172,7 @@ theorem isCoprime_X_sub_C_of_isUnit_sub {R} [CommRing R] {a b : R} (h : IsUnit (
     IsCoprime (X - C a) (X - C b) :=
   ⟨-C h.unit⁻¹.val, C h.unit⁻¹.val, by
     rw [neg_mul_comm, ← left_distrib, neg_add_eq_sub, sub_sub_sub_cancel_left, ← C_sub, ← C_mul]
-    rw [←C_1]
+    rw [← C_1]
     congr
     exact h.val_inv_mul⟩
 set_option linter.uppercaseLean3 false in

We still have the exact_mod_cast tactic, used in a few places, which somehow (?) works a little bit harder to prevent the expected type influencing the elaboration of the term. I would like to get to the bottom of this, and it will be easier once the only usages of exact_mod_cast are the ones that don't work using the term elaborator by itself.

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

@@ -510,7 +510,7 @@ theorem exists_multiset_roots [DecidableEq R] :
         calc
           (card (x ::ₘ t) : WithBot ℕ) = Multiset.card t + 1 := by
             congr
-            exact_mod_cast Multiset.card_cons _ _
+            exact mod_cast Multiset.card_cons _ _
           _ ≤ degree p := by
             rw [← degree_add_divByMonic (monic_X_sub_C x) hdeg, degree_X_sub_C, add_comm];
               exact add_le_add (le_refl (1 : WithBot ℕ)) htd,

PR contents

This is the supremum of

• #8284
• #8056
• #8023
• #8332
• #8226 (already approved)
• #7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

• leanprover/lean4#2778
• leanprover/lean4#2790
• leanprover/lean4#2783
• leanprover/lean4#2825
• leanprover/lean4#2722

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

• switching to using explicit lemmas that have the intended level of application
• (config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
• Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

@@ -1300,7 +1300,7 @@ theorem count_map_roots_of_injective [IsDomain A] [DecidableEq B] (p : A[X]) {f
     (p.roots.map f).count b ≤ rootMultiplicity b (p.map f) := by
   by_cases hp0 : p = 0
   · simp only [hp0, roots_zero, Multiset.map_zero, Multiset.count_zero, Polynomial.map_zero,
-      rootMultiplicity_zero]
+      rootMultiplicity_zero, le_refl]
   · exact count_map_roots ((Polynomial.map_ne_zero_iff hf).mpr hp0) b
 #align polynomial.count_map_roots_of_injective Polynomial.count_map_roots_of_injective
 
@@ -1328,7 +1328,7 @@ theorem card_roots_le_map [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (
 theorem card_roots_le_map_of_injective [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B}
     (hf : Function.Injective f) : Multiset.card p.roots ≤ Multiset.card (p.map f).roots := by
   by_cases hp0 : p = 0
-  · simp only [hp0, roots_zero, Polynomial.map_zero, Multiset.card_zero]
+  · simp only [hp0, roots_zero, Polynomial.map_zero, Multiset.card_zero]; rfl
   exact card_roots_le_map ((Polynomial.map_ne_zero_iff hf).mpr hp0)
 #align polynomial.card_roots_le_map_of_injective Polynomial.card_roots_le_map_of_injective
 

This eliminates (fun a ↦ β) α in the type when applying a FunLike.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -1328,7 +1328,7 @@ theorem card_roots_le_map [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (
 theorem card_roots_le_map_of_injective [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B}
     (hf : Function.Injective f) : Multiset.card p.roots ≤ Multiset.card (p.map f).roots := by
   by_cases hp0 : p = 0
-  · simp only [hp0, roots_zero, Polynomial.map_zero, Multiset.card_zero]; rfl
+  · simp only [hp0, roots_zero, Polynomial.map_zero, Multiset.card_zero]
   exact card_roots_le_map ((Polynomial.map_ne_zero_iff hf).mpr hp0)
 #align polynomial.card_roots_le_map_of_injective Polynomial.card_roots_le_map_of_injective
 

Adds two lemmas that show that negation and subtraction commute with polynomial division.

Co-authored-by: Andrés Goens <andres@goens.org> Co-authored-by: Andrés Goens <andres.goens@ed.ac.uk>

@@ -105,6 +105,12 @@ def modByMonicHom (q : R[X]) : R[X] →ₗ[R] R[X] where
   map_smul' := smul_modByMonic
 #align polynomial.mod_by_monic_hom Polynomial.modByMonicHom
 
+theorem neg_modByMonic (p mod : R[X]) : (-p) %ₘ mod = - (p %ₘ mod) :=
+  (modByMonicHom mod).map_neg p
+
+theorem sub_modByMonic (a b mod : R[X]) : (a - b) %ₘ mod = a %ₘ mod - b %ₘ mod :=
+  (modByMonicHom mod).map_sub a b
+
 end
 
 section

This doesn't change any polynomial operations, but:

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

This is exhaustive, within the directories it touches.

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

@@ -370,7 +370,7 @@ introduced `Polynomial.rootMultiplicity_eq_nat_find_of_nonzero` to contain the i
 theorem le_rootMultiplicity_iff {p : R[X]} (p0 : p ≠ 0) {a : R} {n : ℕ} :
     n ≤ rootMultiplicity a p ↔ (X - C a) ^ n ∣ p := by
   classical
-  rw [rootMultiplicity_eq_nat_find_of_nonzero p0, Nat.le_find_iff]
+  rw [rootMultiplicity_eq_nat_find_of_nonzero p0, @Nat.le_find_iff _ (_)]
   simp_rw [Classical.not_not]
   refine ⟨fun h => ?_, fun h m hm => (pow_dvd_pow _ hm).trans h⟩
   cases' n with n;

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

@@ -912,17 +912,100 @@ theorem funext [Infinite R] {p q : R[X]} (ext : ∀ r : R, p.eval r = q.eval r)
 
 variable [CommRing T]
 
-/-- The set of distinct roots of `p` in `E`.
+/-- Given a polynomial `p` with coefficients in a ring `T` and a `T`-algebra `S`, `aroots p S` is
+the multiset of roots of `p` regarded as a polynomial over `S`. -/
+noncomputable abbrev aroots (p : T[X]) (S) [CommRing S] [IsDomain S] [Algebra T S] : Multiset S :=
+  (p.map (algebraMap T S)).roots
 
-If you have a non-separable polynomial, use `Polynomial.roots` for the multiset
+theorem aroots_def (p : T[X]) (S) [CommRing S] [IsDomain S] [Algebra T S] :
+    p.aroots S = (p.map (algebraMap T S)).roots :=
+  rfl
+
+theorem mem_aroots' [CommRing S] [IsDomain S] [Algebra T S] {p : T[X]} {a : S} :
+    a ∈ p.aroots S ↔ p.map (algebraMap T S) ≠ 0 ∧ aeval a p = 0 := by
+  rw [mem_roots', IsRoot.def, ← eval₂_eq_eval_map, aeval_def]
+
+theorem mem_aroots [CommRing S] [IsDomain S] [Algebra T S]
+    [NoZeroSMulDivisors T S] {p : T[X]} {a : S} : a ∈ p.aroots S ↔ p ≠ 0 ∧ aeval a p = 0 := by
+  rw [mem_aroots', Polynomial.map_ne_zero_iff]
+  exact NoZeroSMulDivisors.algebraMap_injective T S
+
+theorem aroots_mul [CommRing S] [IsDomain S] [Algebra T S]
+    [NoZeroSMulDivisors T S] {p q : T[X]} (hpq : p * q ≠ 0) :
+    (p * q).aroots S = p.aroots S + q.aroots S := by
+  suffices : map (algebraMap T S) p * map (algebraMap T S) q ≠ 0
+  · rw [aroots_def, Polynomial.map_mul, roots_mul this]
+  rwa [← Polynomial.map_mul, Polynomial.map_ne_zero_iff
+    (NoZeroSMulDivisors.algebraMap_injective T S)]
+
+@[simp]
+theorem aroots_X_sub_C [CommRing S] [IsDomain S] [Algebra T S]
+    (r : T) : aroots (X - C r) S = {algebraMap T S r} := by
+  rw [aroots_def, Polynomial.map_sub, map_X, map_C, roots_X_sub_C]
+
+@[simp]
+theorem aroots_X [CommRing S] [IsDomain S] [Algebra T S] :
+    aroots (X : T[X]) S = {0} := by
+  rw [aroots_def, map_X, roots_X]
+
+@[simp]
+theorem aroots_C [CommRing S] [IsDomain S] [Algebra T S] (a : T) : (C a).aroots S = 0 := by
+  rw [aroots_def, map_C, roots_C]
+
+@[simp]
+theorem aroots_zero (S) [CommRing S] [IsDomain S] [Algebra T S] : (0 : T[X]).aroots S = 0 := by
+  rw [← C_0, aroots_C]
+
+@[simp]
+theorem aroots_one [CommRing S] [IsDomain S] [Algebra T S] :
+    (1 : T[X]).aroots S = 0 :=
+  aroots_C 1
+
+@[simp]
+theorem aroots_C_mul [CommRing S] [IsDomain S] [Algebra T S]
+    [NoZeroSMulDivisors T S] {a : T} (p : T[X]) (ha : a ≠ 0) :
+    (C a * p).aroots S = p.aroots S := by
+  rw [aroots_def, Polynomial.map_mul, map_C, roots_C_mul]
+  rwa [map_ne_zero_iff]
+  exact NoZeroSMulDivisors.algebraMap_injective T S
+
+@[simp]
+theorem aroots_smul_nonzero [CommRing S] [IsDomain S] [Algebra T S]
+    [NoZeroSMulDivisors T S] {a : T} (p : T[X]) (ha : a ≠ 0) :
+    (a • p).aroots S = p.aroots S := by
+  rw [smul_eq_C_mul, aroots_C_mul _ ha]
+
+@[simp]
+theorem aroots_pow [CommRing S] [IsDomain S] [Algebra T S] (p : T[X]) (n : ℕ) :
+    (p ^ n).aroots S = n • p.aroots S := by
+  rw [aroots_def, Polynomial.map_pow, roots_pow]
+
+theorem aroots_X_pow [CommRing S] [IsDomain S] [Algebra T S] (n : ℕ) :
+    (X ^ n : T[X]).aroots S = n • ({0} : Multiset S) := by
+  rw [aroots_pow, aroots_X]
+
+theorem aroots_C_mul_X_pow [CommRing S] [IsDomain S] [Algebra T S]
+    [NoZeroSMulDivisors T S] {a : T} (ha : a ≠ 0) (n : ℕ) :
+    (C a * X ^ n : T[X]).aroots S = n • ({0} : Multiset S) := by
+  rw [aroots_C_mul _ ha, aroots_X_pow]
+
+@[simp]
+theorem aroots_monomial [CommRing S] [IsDomain S] [Algebra T S]
+    [NoZeroSMulDivisors T S] {a : T} (ha : a ≠ 0) (n : ℕ) :
+    (monomial n a).aroots S = n • ({0} : Multiset S) := by
+  rw [← C_mul_X_pow_eq_monomial, aroots_C_mul_X_pow ha]
+
+/-- The set of distinct roots of `p` in `S`.
+
+If you have a non-separable polynomial, use `Polynomial.aroots` for the multiset
 where multiple roots have the appropriate multiplicity. -/
 def rootSet (p : T[X]) (S) [CommRing S] [IsDomain S] [Algebra T S] : Set S :=
   haveI := Classical.decEq S
-  (p.map (algebraMap T S)).roots.toFinset
+  (p.aroots S).toFinset
 #align polynomial.root_set Polynomial.rootSet
 
 theorem rootSet_def (p : T[X]) (S) [CommRing S] [IsDomain S] [Algebra T S] [DecidableEq S] :
-    p.rootSet S = (p.map (algebraMap T S)).roots.toFinset := by
+    p.rootSet S = (p.aroots S).toFinset := by
   rw [rootSet]
   convert rfl
 #align polynomial.root_set_def Polynomial.rootSet_def
@@ -930,7 +1013,7 @@ theorem rootSet_def (p : T[X]) (S) [CommRing S] [IsDomain S] [Algebra T S] [Deci
 @[simp]
 theorem rootSet_C [CommRing S] [IsDomain S] [Algebra T S] (a : T) : (C a).rootSet S = ∅ := by
   classical
-  rw [rootSet_def, map_C, roots_C, Multiset.toFinset_zero, Finset.coe_empty]
+  rw [rootSet_def, aroots_C, Multiset.toFinset_zero, Finset.coe_empty]
 set_option linter.uppercaseLean3 false in
 #align polynomial.root_set_C Polynomial.rootSet_C
 
@@ -970,14 +1053,12 @@ theorem bUnion_roots_finite {R S : Type*} [Semiring R] [CommRing S] [IsDomain S]
 theorem mem_rootSet' {p : T[X]} {S : Type*} [CommRing S] [IsDomain S] [Algebra T S] {a : S} :
     a ∈ p.rootSet S ↔ p.map (algebraMap T S) ≠ 0 ∧ aeval a p = 0 := by
   classical
-  rw [rootSet_def, Finset.mem_coe, mem_toFinset, mem_roots', IsRoot.def, ← eval₂_eq_eval_map,
-    aeval_def]
+  rw [rootSet_def, Finset.mem_coe, mem_toFinset, mem_aroots']
 #align polynomial.mem_root_set' Polynomial.mem_rootSet'
 
 theorem mem_rootSet {p : T[X]} {S : Type*} [CommRing S] [IsDomain S] [Algebra T S]
     [NoZeroSMulDivisors T S] {a : S} : a ∈ p.rootSet S ↔ p ≠ 0 ∧ aeval a p = 0 := by
-  rw [mem_rootSet',
-    (map_injective _ (NoZeroSMulDivisors.algebraMap_injective T S)).ne_iff' (Polynomial.map_zero _)]
+  rw [mem_rootSet', Polynomial.map_ne_zero_iff (NoZeroSMulDivisors.algebraMap_injective T S)]
 #align polynomial.mem_root_set Polynomial.mem_rootSet
 
 theorem mem_rootSet_of_ne {p : T[X]} {S : Type*} [CommRing S] [IsDomain S] [Algebra T S]

Also WithBot.charZero

@@ -133,9 +133,8 @@ instance : NoZeroDivisors R[X] where
     rw [← leadingCoeff_zero, ← leadingCoeff_mul, h]
 
 theorem natDegree_mul (hp : p ≠ 0) (hq : q ≠ 0) : (p*q).natDegree = p.natDegree + q.natDegree := by
-  rw [← WithBot.coe_eq_coe, ← Nat.cast_withBot, ←degree_eq_natDegree (mul_ne_zero hp hq),
-    WithBot.coe_add, ← Nat.cast_withBot, ←degree_eq_natDegree hp, ← Nat.cast_withBot,
-    ← degree_eq_natDegree hq, degree_mul]
+  rw [← Nat.cast_inj (R := WithBot ℕ), ←degree_eq_natDegree (mul_ne_zero hp hq),
+    Nat.cast_add,  ←degree_eq_natDegree hp, ← degree_eq_natDegree hq, degree_mul]
 #align polynomial.nat_degree_mul Polynomial.natDegree_mul
 
 theorem trailingDegree_mul : (p * q).trailingDegree = p.trailingDegree + q.trailingDegree := by
@@ -525,8 +524,8 @@ theorem exists_multiset_roots [DecidableEq R] :
 termination_by _ p _ => natDegree p
 decreasing_by {
   simp_wf
-  apply WithBot.coe_lt_coe.mp
-  simp only [degree_eq_natDegree hp, degree_eq_natDegree hd0, ←Nat.cast_withBot] at wf;
+  apply (Nat.cast_lt (α := WithBot ℕ)).mp
+  simp only [degree_eq_natDegree hp, degree_eq_natDegree hd0] at wf;
   assumption}
 #align polynomial.exists_multiset_roots Polynomial.exists_multiset_roots
 
@@ -821,8 +820,7 @@ theorem card_nthRoots (n : ℕ) (a : R) : Multiset.card (nthRoots n a) ≤ n :=
             rw [hn, pow_zero, ← C_1, ← RingHom.map_sub]
             exact degree_C_le))
   else by
-    rw [← WithBot.coe_le_coe]
-    simp only [← Nat.cast_withBot]
+    rw [← Nat.cast_le (α := WithBot ℕ)]
     rw [← degree_X_pow_sub_C (Nat.pos_of_ne_zero hn) a]
     exact card_roots (X_pow_sub_C_ne_zero (Nat.pos_of_ne_zero hn) a))
 #align polynomial.card_nth_roots Polynomial.card_nthRoots

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

@@ -114,7 +114,7 @@ variable [Ring S]
 theorem aeval_modByMonic_eq_self_of_root [Algebra R S] {p q : R[X]} (hq : q.Monic) {x : S}
     (hx : aeval x q = 0) : aeval x (p %ₘ q) = aeval x p := by
     --`eval₂_modByMonic_eq_self_of_root` doesn't work here as it needs commutativity
-  rw [modByMonic_eq_sub_mul_div p hq, _root_.map_sub, _root_.map_mul, hx, MulZeroClass.zero_mul,
+  rw [modByMonic_eq_sub_mul_div p hq, _root_.map_sub, _root_.map_mul, hx, zero_mul,
     sub_zero]
 #align polynomial.aeval_mod_by_monic_eq_self_of_root Polynomial.aeval_modByMonic_eq_self_of_root
 
@@ -140,9 +140,9 @@ theorem natDegree_mul (hp : p ≠ 0) (hq : q ≠ 0) : (p*q).natDegree = p.natDeg
 
 theorem trailingDegree_mul : (p * q).trailingDegree = p.trailingDegree + q.trailingDegree := by
   by_cases hp : p = 0
-  · rw [hp, MulZeroClass.zero_mul, trailingDegree_zero, top_add]
+  · rw [hp, zero_mul, trailingDegree_zero, top_add]
   by_cases hq : q = 0
-  · rw [hq, MulZeroClass.mul_zero, trailingDegree_zero, add_top]
+  · rw [hq, mul_zero, trailingDegree_zero, add_top]
   · rw [trailingDegree_eq_natTrailingDegree hp, trailingDegree_eq_natTrailingDegree hq,
     trailingDegree_eq_natTrailingDegree (mul_ne_zero hp hq), natTrailingDegree_mul hp hq]
     apply WithTop.coe_add
@@ -161,7 +161,7 @@ theorem natDegree_pow (p : R[X]) (n : ℕ) : natDegree (p ^ n) = n * natDegree p
 
 theorem degree_le_mul_left (p : R[X]) (hq : q ≠ 0) : degree p ≤ degree (p * q) := by
   classical
-  exact if hp : p = 0 then by simp only [hp, MulZeroClass.zero_mul, le_refl]
+  exact if hp : p = 0 then by simp only [hp, zero_mul, le_refl]
   else by
     rw [degree_mul, degree_eq_natDegree hp, degree_eq_natDegree hq];
       exact WithBot.coe_le_coe.2 (Nat.le_add_right _ _)
@@ -491,7 +491,7 @@ theorem exists_multiset_roots [DecidableEq R] :
       let ⟨x, hx⟩ := h
       have hpd : 0 < degree p := degree_pos_of_root hp hx
       have hd0 : p /ₘ (X - C x) ≠ 0 := fun h => by
-        rw [← mul_divByMonic_eq_iff_isRoot.2 hx, h, MulZeroClass.mul_zero] at hp; exact hp rfl
+        rw [← mul_divByMonic_eq_iff_isRoot.2 hx, h, mul_zero] at hp; exact hp rfl
       have wf : degree (p /ₘ (X - C x)) < degree p :=
         degree_divByMonic_lt _ (monic_X_sub_C x) hp ((degree_X_sub_C x).symm ▸ by decide)
       let ⟨t, htd, htr⟩ := @exists_multiset_roots _ (p /ₘ (X - C x)) hd0
@@ -698,7 +698,7 @@ theorem roots_one : (1 : R[X]).roots = ∅ :=
 theorem roots_C_mul (p : R[X]) (ha : a ≠ 0) : (C a * p).roots = p.roots := by
   by_cases hp : p = 0 <;>
     simp only [roots_mul, *, Ne.def, mul_eq_zero, C_eq_zero, or_self_iff, not_false_iff, roots_C,
-      zero_add, MulZeroClass.mul_zero]
+      zero_add, mul_zero]
 set_option linter.uppercaseLean3 false in
 #align polynomial.roots_C_mul Polynomial.roots_C_mul
 
@@ -1143,7 +1143,7 @@ theorem exists_prod_multiset_X_sub_C_mul (p : R[X]) :
   obtain ⟨q, he⟩ := p.prod_multiset_X_sub_C_dvd
   use q, he.symm
   obtain rfl | hq := eq_or_ne q 0
-  · rw [MulZeroClass.mul_zero] at he
+  · rw [mul_zero] at he
     subst he
     simp
   constructor

Autoimplicits are highly controversial and also defeat the performance-improving work in #6474.

The intent of this PR is to make autoImplicit opt-in on a per-file basis, by disabling it in the lakefile and enabling it again with set_option autoImplicit true in the few files that rely on it.

That also keeps this PR small, as opposed to attempting to "fix" files to not need it any more.

I claim that many of the uses of autoImplicit in these files are accidental; situations such as:

• Assuming variables are in scope, but pasting the lemma in the wrong section
• Pasting in a lemma from a scratch file without checking to see if the variable names are consistent with the rest of the file
• Making a copy-paste error between lemmas and forgetting to add an explicit arguments.

Having set_option autoImplicit false as the default prevents these types of mistake being made in the 90% of files where autoImplicits are not used at all, and causes them to be caught by CI during review.

I think there were various points during the port where we encouraged porters to delete the universes u v lines; I think having autoparams for universe variables only would cover a lot of the cases we actually use them, while avoiding any real shortcomings.

A Zulip poll (after combining overlapping votes accordingly) was in favor of this change with 5:5:18 as the no:dontcare:yes vote ratio.

While this PR was being reviewed, a handful of files gained some more likely-accidental autoImplicits. In these places, set_option autoImplicit true has been placed locally within a section, rather than at the top of the file.

@@ -31,6 +31,8 @@ This file starts looking like the ring theory of $ R[X] $
 
 -/
 
+set_option autoImplicit true
+
 
 noncomputable section
 

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

This has nice performance benefits.

@@ -718,7 +718,7 @@ theorem roots_multiset_prod (m : Multiset R[X]) : (0 : R[X]) ∉ m → m.prod.ro
   simpa only [Multiset.coe_prod, quot_mk_to_coe''] using roots_list_prod L
 #align polynomial.roots_multiset_prod Polynomial.roots_multiset_prod
 
-theorem roots_prod {ι : Type _} (f : ι → R[X]) (s : Finset ι) :
+theorem roots_prod {ι : Type*} (f : ι → R[X]) (s : Finset ι) :
     s.prod f ≠ 0 → (s.prod f).roots = s.val.bind fun i => roots (f i) := by
   rcases s with ⟨m, hm⟩
   simpa [Multiset.prod_eq_zero_iff, Multiset.bind_map] using roots_multiset_prod (m.map f)
@@ -832,13 +832,13 @@ theorem nthRoots_two_eq_zero_iff {r : R} : nthRoots 2 r = 0 ↔ ¬IsSquare r :=
 #align polynomial.nth_roots_two_eq_zero_iff Polynomial.nthRoots_two_eq_zero_iff
 
 /-- The multiset `nthRoots ↑n (1 : R)` as a Finset. -/
-def nthRootsFinset (n : ℕ) (R : Type _) [CommRing R] [IsDomain R] : Finset R :=
+def nthRootsFinset (n : ℕ) (R : Type*) [CommRing R] [IsDomain R] : Finset R :=
   haveI := Classical.decEq R
   Multiset.toFinset (nthRoots n (1 : R))
 #align polynomial.nth_roots_finset Polynomial.nthRootsFinset
 
 -- porting note: new
-lemma nthRootsFinset_def (n : ℕ) (R : Type _) [CommRing R] [IsDomain R] [DecidableEq R] :
+lemma nthRootsFinset_def (n : ℕ) (R : Type*) [CommRing R] [IsDomain R] [DecidableEq R] :
     nthRootsFinset n R = Multiset.toFinset (nthRoots n (1 : R)) := by
   unfold nthRootsFinset
   convert rfl
@@ -939,19 +939,19 @@ theorem rootSet_zero (S) [CommRing S] [IsDomain S] [Algebra T S] : (0 : T[X]).ro
   rw [← C_0, rootSet_C]
 #align polynomial.root_set_zero Polynomial.rootSet_zero
 
-instance rootSetFintype (p : T[X]) (S : Type _) [CommRing S] [IsDomain S] [Algebra T S] :
+instance rootSetFintype (p : T[X]) (S : Type*) [CommRing S] [IsDomain S] [Algebra T S] :
     Fintype (p.rootSet S) :=
   FinsetCoe.fintype _
 #align polynomial.root_set_fintype Polynomial.rootSetFintype
 
-theorem rootSet_finite (p : T[X]) (S : Type _) [CommRing S] [IsDomain S] [Algebra T S] :
+theorem rootSet_finite (p : T[X]) (S : Type*) [CommRing S] [IsDomain S] [Algebra T S] :
     (p.rootSet S).Finite :=
   Set.toFinite _
 #align polynomial.root_set_finite Polynomial.rootSet_finite
 
 /-- The set of roots of all polynomials of bounded degree and having coefficients in a finite set
 is finite. -/
-theorem bUnion_roots_finite {R S : Type _} [Semiring R] [CommRing S] [IsDomain S] [DecidableEq S]
+theorem bUnion_roots_finite {R S : Type*} [Semiring R] [CommRing S] [IsDomain S] [DecidableEq S]
     (m : R →+* S) (d : ℕ) {U : Set R} (h : U.Finite) :
     (⋃ (f : R[X]) (_ : f.natDegree ≤ d ∧ ∀ i, f.coeff i ∈ U),
         ((f.map m).roots.toFinset.toSet : Set S)).Finite :=
@@ -967,20 +967,20 @@ theorem bUnion_roots_finite {R S : Type _} [Semiring R] [CommRing S] [IsDomain S
     fun i _ => Finset.finite_toSet _
 #align polynomial.bUnion_roots_finite Polynomial.bUnion_roots_finite
 
-theorem mem_rootSet' {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Algebra T S] {a : S} :
+theorem mem_rootSet' {p : T[X]} {S : Type*} [CommRing S] [IsDomain S] [Algebra T S] {a : S} :
     a ∈ p.rootSet S ↔ p.map (algebraMap T S) ≠ 0 ∧ aeval a p = 0 := by
   classical
   rw [rootSet_def, Finset.mem_coe, mem_toFinset, mem_roots', IsRoot.def, ← eval₂_eq_eval_map,
     aeval_def]
 #align polynomial.mem_root_set' Polynomial.mem_rootSet'
 
-theorem mem_rootSet {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Algebra T S]
+theorem mem_rootSet {p : T[X]} {S : Type*} [CommRing S] [IsDomain S] [Algebra T S]
     [NoZeroSMulDivisors T S] {a : S} : a ∈ p.rootSet S ↔ p ≠ 0 ∧ aeval a p = 0 := by
   rw [mem_rootSet',
     (map_injective _ (NoZeroSMulDivisors.algebraMap_injective T S)).ne_iff' (Polynomial.map_zero _)]
 #align polynomial.mem_root_set Polynomial.mem_rootSet
 
-theorem mem_rootSet_of_ne {p : T[X]} {S : Type _} [CommRing S] [IsDomain S] [Algebra T S]
+theorem mem_rootSet_of_ne {p : T[X]} {S : Type*} [CommRing S] [IsDomain S] [Algebra T S]
     [NoZeroSMulDivisors T S] (hp : p ≠ 0) {a : S} : a ∈ p.rootSet S ↔ aeval a p = 0 :=
   mem_rootSet.trans <| and_iff_right hp
 #align polynomial.mem_root_set_of_ne Polynomial.mem_rootSet_of_ne
@@ -1176,7 +1176,7 @@ end CommRing
 
 section
 
-variable {A B : Type _} [CommRing A] [CommRing B]
+variable {A B : Type*} [CommRing A] [CommRing B]
 
 theorem le_rootMultiplicity_map {p : A[X]} {f : A →+* B} (hmap : map f p ≠ 0) (a : A) :
     rootMultiplicity a p ≤ rootMultiplicity (f a) (p.map f) := by

• depends on: #5966

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

@@ -2,11 +2,6 @@
 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, Johan Commelin
-
-! This file was ported from Lean 3 source module data.polynomial.ring_division
-! leanprover-community/mathlib commit 8efcf8022aac8e01df8d302dcebdbc25d6a886c8
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.CharZero.Infinite
 import Mathlib.Data.Polynomial.AlgebraMap
@@ -15,6 +10,8 @@ import Mathlib.Data.Polynomial.Div
 import Mathlib.RingTheory.Localization.FractionRing
 import Mathlib.Algebra.Polynomial.BigOperators
 
+#align_import data.polynomial.ring_division from "leanprover-community/mathlib"@"8efcf8022aac8e01df8d302dcebdbc25d6a886c8"
+
 /-!
 # Theory of univariate polynomials
 

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

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

@@ -365,7 +365,7 @@ variable [CommRing R]
 inferred type and synthesized type for `DecidableRel` when using `Nat.le_find_iff` from
 `Mathlib.Data.Polynomial.Div` After some discussion on [Zulip]
 (https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/decidability.20leakage)
-introduced  `Polynomial.rootMultiplicity_eq_nat_find_of_nonzero` to contain the issue
+introduced `Polynomial.rootMultiplicity_eq_nat_find_of_nonzero` to contain the issue
 -/
 /-- The multiplicity of `a` as root of a nonzero polynomial `p` is at least `n` iff
   `(X - a) ^ n` divides `p`. -/
@@ -1220,7 +1220,7 @@ theorem count_map_roots_of_injective [IsDomain A] [DecidableEq B] (p : A[X]) {f
   · exact count_map_roots ((Polynomial.map_ne_zero_iff hf).mpr hp0) b
 #align polynomial.count_map_roots_of_injective Polynomial.count_map_roots_of_injective
 
-theorem map_roots_le [IsDomain A] [IsDomain B]  {p : A[X]} {f : A →+* B} (h : p.map f ≠ 0) :
+theorem map_roots_le [IsDomain A] [IsDomain B] {p : A[X]} {f : A →+* B} (h : p.map f ≠ 0) :
     p.roots.map f ≤ (p.map f).roots := by
   classical
   exact Multiset.le_iff_count.2 fun b => by

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

@@ -1207,7 +1207,7 @@ theorem count_map_roots [IsDomain A] [DecidableEq B] {p : A[X]} {f : A →+* B}
     (Multiset.prod_dvd_prod_of_le <| Multiset.map_le_map <| Multiset.filter_le (Eq b) _).trans ?_
   convert Polynomial.map_dvd f p.prod_multiset_X_sub_C_dvd
   simp only [Polynomial.map_multiset_prod, Multiset.map_map]
-  congr ; ext1
+  congr; ext1
   simp only [Function.comp_apply, Polynomial.map_sub, map_X, map_C]
 #align polynomial.count_map_roots Polynomial.count_map_roots
 

This PR is the result of running

find . -type f -name "*.lean" -exec sed -i -E 's/^( +)\. /\1· /' {} \;
find . -type f -name "*.lean" -exec sed -i -E 'N;s/^( +·)\n +(.*)$/\1 \2/;P;D' {} \;

which firstly replaces . focusing dots with · and secondly removes isolated instances of such dots, unifying them with the following line. A new rule is placed in the style linter to verify this.

@@ -286,8 +286,7 @@ theorem irreducible_of_monic (hp : p.Monic) (hp1 : p ≠ 1) :
           (isUnit_of_mul_eq_one g _)⟩⟩
   · rwa [Monic, leadingCoeff_mul, leadingCoeff_C, ← leadingCoeff_mul, mul_comm, ← hfg, ← Monic]
   · rwa [Monic, leadingCoeff_mul, leadingCoeff_C, ← leadingCoeff_mul, ← hfg, ← Monic]
-  ·
-    rw [mul_mul_mul_comm, ← C_mul, ← leadingCoeff_mul, ← hfg, hp.leadingCoeff, C_1, mul_one,
+  · rw [mul_mul_mul_comm, ← C_mul, ← leadingCoeff_mul, ← hfg, hp.leadingCoeff, C_1, mul_one,
       mul_comm, ← hfg]
 #align polynomial.irreducible_of_monic Polynomial.irreducible_of_monic
 
@@ -734,8 +733,7 @@ theorem roots_pow (p : R[X]) (n : ℕ) : (p ^ n).roots = n • p.roots := by
   · rw [pow_zero, roots_one, Nat.zero_eq, zero_smul, empty_eq_zero]
   · rcases eq_or_ne p 0 with (rfl | hp)
     · rw [zero_pow n.succ_pos, roots_zero, smul_zero]
-    ·
-      rw [pow_succ', roots_mul (mul_ne_zero (pow_ne_zero _ hp) hp), ihn, Nat.succ_eq_add_one,
+    · rw [pow_succ', roots_mul (mul_ne_zero (pow_ne_zero _ hp) hp), ihn, Nat.succ_eq_add_one,
         add_smul, one_smul]
 #align polynomial.roots_pow Polynomial.roots_pow
 
@@ -897,8 +895,7 @@ theorem comp_eq_zero_iff : p.comp q = 0 ↔ p = 0 ∨ p.eval (q.coeff 0) = 0 ∧
       exact Or.inl (key.trans h)
     · rw [key, comp_C, C_eq_zero] at h
       exact Or.inr ⟨h, key⟩
-  ·
-    exact fun h =>
+  · exact fun h =>
       Or.rec (fun h => by rw [h, zero_comp]) (fun h => by rw [h.2, comp_C, h.1, C_0]) h
 #align polynomial.comp_eq_zero_iff Polynomial.comp_eq_zero_iff
 

We proved that a polynomial is a unit if and only if all of its coefficients are nilpotent, except the constant term which is a unit.

Co-authored-by: Cyprien Chauveau cyprien.chauveau@etu.u-paris.fr Co-authored-by: Lucas Pouillart lucas.pouillart@etu.u-paris.fr

Co-authored-by: EmilieUthaiwat <102412311+EmilieUthaiwat@users.noreply.github.com>

@@ -228,6 +228,8 @@ theorem degree_coe_units [Nontrivial R] (u : R[X]ˣ) : degree (u : R[X]) = 0 :=
   degree_eq_zero_of_isUnit ⟨u, rfl⟩
 #align polynomial.degree_coe_units Polynomial.degree_coe_units
 
+/-- Characterization of a unit of a polynomial ring over an integral domain `R`.
+See `Polynomial.isUnit_iff_coeff_isUnit_isNilpotent` when `R` is a commutative ring. -/
 theorem isUnit_iff : IsUnit p ↔ ∃ r : R, IsUnit r ∧ C r = p :=
   ⟨fun hp =>
     ⟨p.coeff 0,