data.polynomial.splits ⟷ Mathlib.Data.Polynomial.Splits

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

@@ -289,12 +289,12 @@ theorem splits_iff (f : K[X]) :
 #align polynomial.splits_iff Polynomial.splits_iff
 -/
 
-#print Polynomial.Splits.def' /-
+#print Polynomial.Splits.def /-
 /-- This lemma is for polynomials over a field. -/
-theorem Splits.def' {i : K →+* L} {f : K[X]} (h : Splits i f) :
+theorem Splits.def {i : K →+* L} {f : K[X]} (h : Splits i f) :
     f = 0 ∨ ∀ {g : L[X]}, Irreducible g → g ∣ f.map i → degree g = 1 :=
   (splits_iff i f).mp h
-#align polynomial.splits.def Polynomial.Splits.def'
+#align polynomial.splits.def Polynomial.Splits.def
 -/
 
 #print Polynomial.splits_of_splits_mul /-

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

@@ -4,8 +4,8 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 -/
 import Data.List.Prime
-import Data.Polynomial.FieldDivision
-import Data.Polynomial.Lifts
+import Algebra.Polynomial.FieldDivision
+import Algebra.Polynomial.Lifts
 
 #align_import data.polynomial.splits from "leanprover-community/mathlib"@"31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0"
 

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

@@ -289,12 +289,12 @@ theorem splits_iff (f : K[X]) :
 #align polynomial.splits_iff Polynomial.splits_iff
 -/
 
-#print Polynomial.Splits.def /-
+#print Polynomial.Splits.def' /-
 /-- This lemma is for polynomials over a field. -/
-theorem Splits.def {i : K →+* L} {f : K[X]} (h : Splits i f) :
+theorem Splits.def' {i : K →+* L} {f : K[X]} (h : Splits i f) :
     f = 0 ∨ ∀ {g : L[X]}, Irreducible g → g ∣ f.map i → degree g = 1 :=
   (splits_iff i f).mp h
-#align polynomial.splits.def Polynomial.Splits.def
+#align polynomial.splits.def Polynomial.Splits.def'
 -/
 
 #print Polynomial.splits_of_splits_mul /-

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

@@ -77,7 +77,7 @@ theorem splits_of_map_eq_C {f : K[X]} {a : L} (h : f.map i = C a) : Splits i f :
           isUnit_iff_degree_eq_zero.2 <| by
             have := congr_arg degree hp
             rw [h, degree_C ha, degree_mul, @eq_comm (WithBot ℕ) 0, Nat.WithBot.add_eq_zero_iff] at
-              this 
+              this
             exact this.1
 #align polynomial.splits_of_map_eq_C Polynomial.splits_of_map_eq_C
 -/
@@ -94,7 +94,7 @@ theorem splits_of_map_degree_eq_one {f : K[X]} (hf : degree (f.map i) = 1) : Spl
   Or.inr fun g hg ⟨p, hp⟩ => by
     have := congr_arg degree hp <;>
           simp [Nat.WithBot.add_eq_one_iff, hf, @eq_comm (WithBot ℕ) 1,
-            mt is_unit_iff_degree_eq_zero.2 hg.1] at this  <;>
+            mt is_unit_iff_degree_eq_zero.2 hg.1] at this <;>
         clear _fun_match <;>
       tauto
 #align polynomial.splits_of_map_degree_eq_one Polynomial.splits_of_map_degree_eq_one
@@ -104,8 +104,8 @@ theorem splits_of_map_degree_eq_one {f : K[X]} (hf : degree (f.map i) = 1) : Spl
 theorem splits_of_degree_le_one {f : K[X]} (hf : degree f ≤ 1) : Splits i f :=
   if hif : degree (f.map i) ≤ 0 then splits_of_map_eq_C i (degree_le_zero_iff.mp hif)
   else by
-    push_neg at hif 
-    rw [← Order.succ_le_iff, ← WithBot.coe_zero, WithBot.succ_coe, Nat.succ_eq_succ] at hif 
+    push_neg at hif
+    rw [← Order.succ_le_iff, ← WithBot.coe_zero, WithBot.succ_coe, Nat.succ_eq_succ] at hif
     exact splits_of_map_degree_eq_one i (le_antisymm ((degree_map_le i _).trans hf) hif)
 #align polynomial.splits_of_degree_le_one Polynomial.splits_of_degree_le_one
 -/
@@ -185,7 +185,7 @@ theorem splits_prod {ι : Type u} {s : ι → K[X]} {t : Finset ι} :
     (∀ j ∈ t, (s j).Splits i) → (∏ x in t, s x).Splits i :=
   by
   refine' Finset.induction_on t (fun _ => splits_one i) fun a t hat ih ht => _
-  rw [Finset.forall_mem_insert] at ht ; rw [Finset.prod_insert hat]
+  rw [Finset.forall_mem_insert] at ht; rw [Finset.prod_insert hat]
   exact splits_mul i ht.1 (ih ht.2)
 #align polynomial.splits_prod Polynomial.splits_prod
 -/
@@ -229,7 +229,7 @@ theorem roots_ne_zero_of_splits' {f : K[X]} (hs : Splits i f) (hf0 : natDegree (
     (f.map i).roots ≠ 0 :=
   let ⟨x, hx⟩ := exists_root_of_splits' i hs fun h => hf0 <| natDegree_eq_of_degree_eq_some h
   fun h => by
-  rw [← eval_map] at hx 
+  rw [← eval_map] at hx
   cases h.subst ((mem_roots _).2 hx); exact ne_zero_of_nat_degree_gt (Nat.pos_of_ne_zero hf0)
 #align polynomial.roots_ne_zero_of_splits' Polynomial.roots_ne_zero_of_splits'
 -/
@@ -256,14 +256,14 @@ theorem natDegree_eq_card_roots' {p : K[X]} {i : K →+* L} (hsplit : Splits i p
   by_cases hp : p.map i = 0
   · rw [hp, nat_degree_zero, roots_zero, Multiset.card_zero]
   obtain ⟨q, he, hd, hr⟩ := exists_prod_multiset_X_sub_C_mul (p.map i)
-  rw [← splits_id_iff_splits, ← he] at hsplit 
-  rw [← he] at hp 
+  rw [← splits_id_iff_splits, ← he] at hsplit
+  rw [← he] at hp
   have hq : q ≠ 0 := fun h => hp (by rw [h, MulZeroClass.mul_zero])
   rw [← hd, add_right_eq_self]
   by_contra
   have h' : (map (RingHom.id L) q).natDegree ≠ 0 := by simp [h]
   have := roots_ne_zero_of_splits' (RingHom.id L) (splits_of_splits_mul' _ _ hsplit).2 h'
-  · rw [map_id] at this ; exact this hr
+  · rw [map_id] at this; exact this hr
   · rw [map_id]; exact mul_ne_zero monic_prod_multiset_X_sub_C.ne_zero hq
 #align polynomial.nat_degree_eq_card_roots' Polynomial.natDegree_eq_card_roots'
 -/
@@ -492,8 +492,8 @@ theorem splits_of_exists_multiset {f : K[X]} {s : Multiset L}
   if hf0 : f = 0 then hf0.symm ▸ splits_zero i
   else
     Or.inr fun p hp hdp => by
-      rw [irreducible_iff_prime] at hp 
-      rw [hs, ← Multiset.prod_toList] at hdp 
+      rw [irreducible_iff_prime] at hp
+      rw [hs, ← Multiset.prod_toList] at hdp
       obtain hd | hd := hp.2.2 _ _ hdp
       · refine' (hp.2.1 <| isUnit_of_dvd_unit hd _).elim
         exact is_unit_C.2 ((leading_coeff_ne_zero.2 hf0).IsUnit.map i)
@@ -531,9 +531,9 @@ theorem splits_iff_exists_multiset {f : K[X]} :
 #print Polynomial.splits_comp_of_splits /-
 theorem splits_comp_of_splits (j : L →+* F) {f : K[X]} (h : Splits i f) : Splits (j.comp i) f :=
   by
-  change i with (RingHom.id _).comp i at h 
+  change i with (RingHom.id _).comp i at h
   rw [← splits_map_iff]
-  rw [← splits_map_iff i] at h 
+  rw [← splits_map_iff i] at h
   exact splits_of_splits_id _ h
 #align polynomial.splits_comp_of_splits Polynomial.splits_comp_of_splits
 -/

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

@@ -133,7 +133,7 @@ theorem splits_mul {f g : K[X]} (hf : Splits i f) (hg : Splits i g) : Splits i (
   if h : (f * g).map i = 0 then Or.inl h
   else
     Or.inr fun p hp hpf =>
-      ((PrincipalIdealRing.irreducible_iff_prime.1 hp).2.2 _ _
+      ((irreducible_iff_prime.1 hp).2.2 _ _
             (show p ∣ map i f * map i g by convert hpf <;> rw [Polynomial.map_mul])).elim
         (hf.resolve_left (fun hf => by simpa [hf] using h) hp)
         (hg.resolve_left (fun hg => by simpa [hg] using h) hp)

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

@@ -413,7 +413,10 @@ theorem roots_map {f : K[X]} (hf : f.Splits <| RingHom.id K) : (f.map i).roots =
 
 #print Polynomial.image_rootSet /-
 theorem image_rootSet [Algebra F K] [Algebra F L] {p : F[X]} (h : p.Splits (algebraMap F K))
-    (f : K →ₐ[F] L) : f '' p.rootSet K = p.rootSet L := by classical
+    (f : K →ₐ[F] L) : f '' p.rootSet K = p.rootSet L := by
+  classical rw [root_set, ← Finset.coe_image, ← Multiset.toFinset_map, ← f.coe_to_ring_hom, ←
+    roots_map (↑f) ((splits_id_iff_splits (algebraMap F K)).mpr h), map_map, f.comp_algebra_map, ←
+    root_set]
 #align polynomial.image_root_set Polynomial.image_rootSet
 -/
 

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

@@ -413,10 +413,7 @@ theorem roots_map {f : K[X]} (hf : f.Splits <| RingHom.id K) : (f.map i).roots =
 
 #print Polynomial.image_rootSet /-
 theorem image_rootSet [Algebra F K] [Algebra F L] {p : F[X]} (h : p.Splits (algebraMap F K))
-    (f : K →ₐ[F] L) : f '' p.rootSet K = p.rootSet L := by
-  classical rw [root_set, ← Finset.coe_image, ← Multiset.toFinset_map, ← f.coe_to_ring_hom, ←
-    roots_map (↑f) ((splits_id_iff_splits (algebraMap F K)).mpr h), map_map, f.comp_algebra_map, ←
-    root_set]
+    (f : K →ₐ[F] L) : f '' p.rootSet K = p.rootSet L := by classical
 #align polynomial.image_root_set Polynomial.image_rootSet
 -/
 

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

@@ -3,9 +3,9 @@ Copyright (c) 2018 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 -/
-import Mathbin.Data.List.Prime
-import Mathbin.Data.Polynomial.FieldDivision
-import Mathbin.Data.Polynomial.Lifts
+import Data.List.Prime
+import Data.Polynomial.FieldDivision
+import Data.Polynomial.Lifts
 
 #align_import data.polynomial.splits from "leanprover-community/mathlib"@"31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0"
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2018 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
-
-! This file was ported from Lean 3 source module data.polynomial.splits
-! leanprover-community/mathlib commit 31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.List.Prime
 import Mathbin.Data.Polynomial.FieldDivision
 import Mathbin.Data.Polynomial.Lifts
 
+#align_import data.polynomial.splits from "leanprover-community/mathlib"@"31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0"
+
 /-!
 # Split polynomials
 

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

@@ -70,6 +70,7 @@ theorem splits_zero : Splits i (0 : K[X]) :=
 #align polynomial.splits_zero Polynomial.splits_zero
 -/
 
+#print Polynomial.splits_of_map_eq_C /-
 theorem splits_of_map_eq_C {f : K[X]} {a : L} (h : f.map i = C a) : Splits i f :=
   if ha : a = 0 then Or.inl (h.trans (ha.symm ▸ C_0))
   else
@@ -82,11 +83,14 @@ theorem splits_of_map_eq_C {f : K[X]} {a : L} (h : f.map i = C a) : Splits i f :
               this 
             exact this.1
 #align polynomial.splits_of_map_eq_C Polynomial.splits_of_map_eq_C
+-/
 
+#print Polynomial.splits_C /-
 @[simp]
 theorem splits_C (a : K) : Splits i (C a) :=
   splits_of_map_eq_C i (map_C i)
 #align polynomial.splits_C Polynomial.splits_C
+-/
 
 #print Polynomial.splits_of_map_degree_eq_one /-
 theorem splits_of_map_degree_eq_one {f : K[X]} (hf : degree (f.map i) = 1) : Splits i f :=
@@ -161,13 +165,17 @@ theorem splits_one : Splits i 1 :=
 #align polynomial.splits_one Polynomial.splits_one
 -/
 
+#print Polynomial.splits_of_isUnit /-
 theorem splits_of_isUnit [IsDomain K] {u : K[X]} (hu : IsUnit u) : u.Splits i :=
   (isUnit_iff.mp hu).choose_spec.2 ▸ splits_C _ _
 #align polynomial.splits_of_is_unit Polynomial.splits_of_isUnit
+-/
 
+#print Polynomial.splits_X_sub_C /-
 theorem splits_X_sub_C {x : K} : (X - C x).Splits i :=
   splits_of_degree_le_one _ <| degree_X_sub_C_le _
 #align polynomial.splits_X_sub_C Polynomial.splits_X_sub_C
+-/
 
 #print Polynomial.splits_X /-
 theorem splits_X : X.Splits i :=
@@ -185,15 +193,19 @@ theorem splits_prod {ι : Type u} {s : ι → K[X]} {t : Finset ι} :
 #align polynomial.splits_prod Polynomial.splits_prod
 -/
 
+#print Polynomial.splits_pow /-
 theorem splits_pow {f : K[X]} (hf : f.Splits i) (n : ℕ) : (f ^ n).Splits i :=
   by
   rw [← Finset.card_range n, ← Finset.prod_const]
   exact splits_prod i fun j hj => hf
 #align polynomial.splits_pow Polynomial.splits_pow
+-/
 
+#print Polynomial.splits_X_pow /-
 theorem splits_X_pow (n : ℕ) : (X ^ n).Splits i :=
   splits_pow i (splits_X i) n
 #align polynomial.splits_X_pow Polynomial.splits_X_pow
+-/
 
 #print Polynomial.splits_id_iff_splits /-
 theorem splits_id_iff_splits {f : K[X]} : (f.map i).Splits (RingHom.id L) ↔ f.Splits i := by
@@ -201,6 +213,7 @@ theorem splits_id_iff_splits {f : K[X]} : (f.map i).Splits (RingHom.id L) ↔ f.
 #align polynomial.splits_id_iff_splits Polynomial.splits_id_iff_splits
 -/
 
+#print Polynomial.exists_root_of_splits' /-
 theorem exists_root_of_splits' {f : K[X]} (hs : Splits i f) (hf0 : degree (f.map i) ≠ 0) :
     ∃ x, eval₂ i x f = 0 :=
   if hf0' : f.map i = 0 then by simp [eval₂_eq_eval_map, hf0']
@@ -212,6 +225,7 @@ theorem exists_root_of_splits' {f : K[X]} (hs : Splits i f) (hf0 : degree (f.map
     let ⟨i, hi⟩ := hg.2
     ⟨x, by rw [← eval_map, hi, eval_mul, show _ = _ from hx, MulZeroClass.zero_mul]⟩
 #align polynomial.exists_root_of_splits' Polynomial.exists_root_of_splits'
+-/
 
 #print Polynomial.roots_ne_zero_of_splits' /-
 theorem roots_ne_zero_of_splits' {f : K[X]} (hs : Splits i f) (hf0 : natDegree (f.map i) ≠ 0) :
@@ -231,11 +245,14 @@ def rootOfSplits' {f : K[X]} (hf : f.Splits i) (hfd : (f.map i).degree ≠ 0) :
 #align polynomial.root_of_splits' Polynomial.rootOfSplits'
 -/
 
+#print Polynomial.map_rootOfSplits' /-
 theorem map_rootOfSplits' {f : K[X]} (hf : f.Splits i) (hfd) :
     f.eval₂ i (rootOfSplits' i hf hfd) = 0 :=
   Classical.choose_spec <| exists_root_of_splits' i hf hfd
 #align polynomial.map_root_of_splits' Polynomial.map_rootOfSplits'
+-/
 
+#print Polynomial.natDegree_eq_card_roots' /-
 theorem natDegree_eq_card_roots' {p : K[X]} {i : K →+* L} (hsplit : Splits i p) :
     (p.map i).natDegree = (p.map i).roots.card :=
   by
@@ -252,11 +269,14 @@ theorem natDegree_eq_card_roots' {p : K[X]} {i : K →+* L} (hsplit : Splits i p
   · rw [map_id] at this ; exact this hr
   · rw [map_id]; exact mul_ne_zero monic_prod_multiset_X_sub_C.ne_zero hq
 #align polynomial.nat_degree_eq_card_roots' Polynomial.natDegree_eq_card_roots'
+-/
 
+#print Polynomial.degree_eq_card_roots' /-
 theorem degree_eq_card_roots' {p : K[X]} {i : K →+* L} (p_ne_zero : p.map i ≠ 0)
     (hsplit : Splits i p) : (p.map i).degree = (p.map i).roots.card := by
   rw [degree_eq_nat_degree p_ne_zero, nat_degree_eq_card_roots' hsplit]
 #align polynomial.degree_eq_card_roots' Polynomial.degree_eq_card_roots'
+-/
 
 end CommRing
 
@@ -264,17 +284,21 @@ variable [Field K] [Field L] [Field F]
 
 variable (i : K →+* L)
 
+#print Polynomial.splits_iff /-
 /-- This lemma is for polynomials over a field. -/
 theorem splits_iff (f : K[X]) :
     Splits i f ↔ f = 0 ∨ ∀ {g : L[X]}, Irreducible g → g ∣ f.map i → degree g = 1 := by
   rw [splits, map_eq_zero]
 #align polynomial.splits_iff Polynomial.splits_iff
+-/
 
+#print Polynomial.Splits.def /-
 /-- This lemma is for polynomials over a field. -/
 theorem Splits.def {i : K →+* L} {f : K[X]} (h : Splits i f) :
     f = 0 ∨ ∀ {g : L[X]}, Irreducible g → g ∣ f.map i → degree g = 1 :=
   (splits_iff i f).mp h
 #align polynomial.splits.def Polynomial.Splits.def
+-/
 
 #print Polynomial.splits_of_splits_mul /-
 theorem splits_of_splits_mul {f g : K[X]} (hfg : f * g ≠ 0) (h : Splits i (f * g)) :
@@ -289,15 +313,19 @@ theorem splits_of_splits_of_dvd {f g : K[X]} (hf0 : f ≠ 0) (hf : Splits i f) (
 #align polynomial.splits_of_splits_of_dvd Polynomial.splits_of_splits_of_dvd
 -/
 
+#print Polynomial.splits_of_splits_gcd_left /-
 theorem splits_of_splits_gcd_left {f g : K[X]} (hf0 : f ≠ 0) (hf : Splits i f) :
     Splits i (EuclideanDomain.gcd f g) :=
   Polynomial.splits_of_splits_of_dvd i hf0 hf (EuclideanDomain.gcd_dvd_left f g)
 #align polynomial.splits_of_splits_gcd_left Polynomial.splits_of_splits_gcd_left
+-/
 
+#print Polynomial.splits_of_splits_gcd_right /-
 theorem splits_of_splits_gcd_right {f g : K[X]} (hg0 : g ≠ 0) (hg : Splits i g) :
     Splits i (EuclideanDomain.gcd f g) :=
   Polynomial.splits_of_splits_of_dvd i hg0 hg (EuclideanDomain.gcd_dvd_right f g)
 #align polynomial.splits_of_splits_gcd_right Polynomial.splits_of_splits_gcd_right
+-/
 
 #print Polynomial.splits_mul_iff /-
 theorem splits_mul_iff {f g : K[X]} (hf : f ≠ 0) (hg : g ≠ 0) :
@@ -318,6 +346,7 @@ theorem splits_prod_iff {ι : Type u} {s : ι → K[X]} {t : Finset ι} :
 #align polynomial.splits_prod_iff Polynomial.splits_prod_iff
 -/
 
+#print Polynomial.degree_eq_one_of_irreducible_of_splits /-
 theorem degree_eq_one_of_irreducible_of_splits {p : K[X]} (hp : Irreducible p)
     (hp_splits : Splits (RingHom.id K) p) : p.degree = 1 :=
   by
@@ -325,11 +354,14 @@ theorem degree_eq_one_of_irreducible_of_splits {p : K[X]} (hp : Irreducible p)
   · exfalso; simp_all
   · apply hp_splits hp; simp
 #align polynomial.degree_eq_one_of_irreducible_of_splits Polynomial.degree_eq_one_of_irreducible_of_splits
+-/
 
+#print Polynomial.exists_root_of_splits /-
 theorem exists_root_of_splits {f : K[X]} (hs : Splits i f) (hf0 : degree f ≠ 0) :
     ∃ x, eval₂ i x f = 0 :=
   exists_root_of_splits' i hs ((f.degree_map i).symm ▸ hf0)
 #align polynomial.exists_root_of_splits Polynomial.exists_root_of_splits
+-/
 
 #print Polynomial.roots_ne_zero_of_splits /-
 theorem roots_ne_zero_of_splits {f : K[X]} (hs : Splits i f) (hf0 : natDegree f ≠ 0) :
@@ -354,33 +386,44 @@ theorem rootOfSplits'_eq_rootOfSplits {f : K[X]} (hf : f.Splits i) (hfd) :
 #align polynomial.root_of_splits'_eq_root_of_splits Polynomial.rootOfSplits'_eq_rootOfSplits
 -/
 
+#print Polynomial.map_rootOfSplits /-
 theorem map_rootOfSplits {f : K[X]} (hf : f.Splits i) (hfd) :
     f.eval₂ i (rootOfSplits i hf hfd) = 0 :=
   map_rootOfSplits' i hf (ne_of_eq_of_ne (degree_map f i) hfd)
 #align polynomial.map_root_of_splits Polynomial.map_rootOfSplits
+-/
 
+#print Polynomial.natDegree_eq_card_roots /-
 theorem natDegree_eq_card_roots {p : K[X]} {i : K →+* L} (hsplit : Splits i p) :
     p.natDegree = (p.map i).roots.card :=
   (natDegree_map i).symm.trans <| natDegree_eq_card_roots' hsplit
 #align polynomial.nat_degree_eq_card_roots Polynomial.natDegree_eq_card_roots
+-/
 
+#print Polynomial.degree_eq_card_roots /-
 theorem degree_eq_card_roots {p : K[X]} {i : K →+* L} (p_ne_zero : p ≠ 0) (hsplit : Splits i p) :
     p.degree = (p.map i).roots.card := by
   rw [degree_eq_nat_degree p_ne_zero, nat_degree_eq_card_roots hsplit]
 #align polynomial.degree_eq_card_roots Polynomial.degree_eq_card_roots
+-/
 
+#print Polynomial.roots_map /-
 theorem roots_map {f : K[X]} (hf : f.Splits <| RingHom.id K) : (f.map i).roots = f.roots.map i :=
   (roots_map_of_injective_of_card_eq_natDegree i.Injective <| by
       convert (nat_degree_eq_card_roots hf).symm; rw [map_id]).symm
 #align polynomial.roots_map Polynomial.roots_map
+-/
 
+#print Polynomial.image_rootSet /-
 theorem image_rootSet [Algebra F K] [Algebra F L] {p : F[X]} (h : p.Splits (algebraMap F K))
     (f : K →ₐ[F] L) : f '' p.rootSet K = p.rootSet L := by
   classical rw [root_set, ← Finset.coe_image, ← Multiset.toFinset_map, ← f.coe_to_ring_hom, ←
     roots_map (↑f) ((splits_id_iff_splits (algebraMap F K)).mpr h), map_map, f.comp_algebra_map, ←
     root_set]
 #align polynomial.image_root_set Polynomial.image_rootSet
+-/
 
+#print Polynomial.adjoin_rootSet_eq_range /-
 theorem adjoin_rootSet_eq_range [Algebra F K] [Algebra F L] {p : F[X]}
     (h : p.Splits (algebraMap F K)) (f : K →ₐ[F] L) :
     Algebra.adjoin F (p.rootSet L) = f.range ↔ Algebra.adjoin F (p.rootSet K) = ⊤ :=
@@ -388,7 +431,9 @@ theorem adjoin_rootSet_eq_range [Algebra F K] [Algebra F L] {p : F[X]}
   rw [← image_root_set h f, Algebra.adjoin_image, ← Algebra.map_top]
   exact (Subalgebra.map_injective f.to_ring_hom.injective).eq_iff
 #align polynomial.adjoin_root_set_eq_range Polynomial.adjoin_rootSet_eq_range
+-/
 
+#print Polynomial.eq_prod_roots_of_splits /-
 theorem eq_prod_roots_of_splits {p : K[X]} {i : K →+* L} (hsplit : Splits i p) :
     p.map i = C (i p.leadingCoeff) * ((p.map i).roots.map fun a => X - C a).Prod :=
   by
@@ -396,19 +441,25 @@ theorem eq_prod_roots_of_splits {p : K[X]} {i : K →+* L} (hsplit : Splits i p)
   apply C_leading_coeff_mul_prod_multiset_X_sub_C
   rw [nat_degree_map]; exact (nat_degree_eq_card_roots hsplit).symm
 #align polynomial.eq_prod_roots_of_splits Polynomial.eq_prod_roots_of_splits
+-/
 
+#print Polynomial.eq_prod_roots_of_splits_id /-
 theorem eq_prod_roots_of_splits_id {p : K[X]} (hsplit : Splits (RingHom.id K) p) :
     p = C p.leadingCoeff * (p.roots.map fun a => X - C a).Prod := by
   simpa using eq_prod_roots_of_splits hsplit
 #align polynomial.eq_prod_roots_of_splits_id Polynomial.eq_prod_roots_of_splits_id
+-/
 
+#print Polynomial.eq_prod_roots_of_monic_of_splits_id /-
 theorem eq_prod_roots_of_monic_of_splits_id {p : K[X]} (m : Monic p)
     (hsplit : Splits (RingHom.id K) p) : p = (p.roots.map fun a => X - C a).Prod :=
   by
   convert eq_prod_roots_of_splits_id hsplit
   simp [m]
 #align polynomial.eq_prod_roots_of_monic_of_splits_id Polynomial.eq_prod_roots_of_monic_of_splits_id
+-/
 
+#print Polynomial.eq_X_sub_C_of_splits_of_single_root /-
 theorem eq_X_sub_C_of_splits_of_single_root {x : K} {h : K[X]} (h_splits : Splits i h)
     (h_roots : (h.map i).roots = {i x}) : h = C h.leadingCoeff * (X - C x) :=
   by
@@ -416,7 +467,9 @@ theorem eq_X_sub_C_of_splits_of_single_root {x : K} {h : K[X]} (h_splits : Split
   rw [eq_prod_roots_of_splits h_splits, h_roots]
   simp
 #align polynomial.eq_X_sub_C_of_splits_of_single_root Polynomial.eq_X_sub_C_of_splits_of_single_root
+-/
 
+#print Polynomial.mem_lift_of_splits_of_roots_mem_range /-
 theorem mem_lift_of_splits_of_roots_mem_range (R : Type _) [CommRing R] [Algebra R K] {f : K[X]}
     (hs : f.Splits (RingHom.id K)) (hm : f.Monic) (hr : ∀ a ∈ f.roots, a ∈ (algebraMap R K).range) :
     f ∈ Polynomial.lifts (algebraMap R K) :=
@@ -426,16 +479,17 @@ theorem mem_lift_of_splits_of_roots_mem_range (R : Type _) [CommRing R] [Algebra
   obtain ⟨b, hb, rfl⟩ := Multiset.mem_map.1 hP
   exact Subring.sub_mem _ (X_mem_lifts _) (C'_mem_lifts (hr _ hb))
 #align polynomial.mem_lift_of_splits_of_roots_mem_range Polynomial.mem_lift_of_splits_of_roots_mem_range
+-/
 
 section UFD
 
 attribute [local instance 10] PrincipalIdealRing.to_uniqueFactorizationMonoid
 
--- mathport name: «expr ~ᵤ »
 local infixl:50 " ~ᵤ " => Associated
 
 open UniqueFactorizationMonoid Associates
 
+#print Polynomial.splits_of_exists_multiset /-
 theorem splits_of_exists_multiset {f : K[X]} {s : Multiset L}
     (hs : f.map i = C (i f.leadingCoeff) * (s.map fun a : L => X - C a).Prod) : Splits i f :=
   if hf0 : f = 0 then hf0.symm ▸ splits_zero i
@@ -451,6 +505,7 @@ theorem splits_of_exists_multiset {f : K[X]} {s : Multiset L}
         rw [degree_eq_degree_of_associated ((hp.dvd_prime_iff_associated <| prime_X_sub_C a).1 hd)]
         exact degree_X_sub_C a
 #align polynomial.splits_of_exists_multiset Polynomial.splits_of_exists_multiset
+-/
 
 #print Polynomial.splits_of_splits_id /-
 theorem splits_of_splits_id {f : K[X]} : Splits (RingHom.id K) f → Splits i f :=
@@ -467,12 +522,14 @@ theorem splits_of_splits_id {f : K[X]} : Splits (RingHom.id K) f → Splits i f
 
 end UFD
 
+#print Polynomial.splits_iff_exists_multiset /-
 theorem splits_iff_exists_multiset {f : K[X]} :
     Splits i f ↔
       ∃ s : Multiset L, f.map i = C (i f.leadingCoeff) * (s.map fun a : L => X - C a).Prod :=
   ⟨fun hf => ⟨(f.map i).roots, eq_prod_roots_of_splits hf⟩, fun ⟨s, hs⟩ =>
     splits_of_exists_multiset i hs⟩
 #align polynomial.splits_iff_exists_multiset Polynomial.splits_iff_exists_multiset
+-/
 
 #print Polynomial.splits_comp_of_splits /-
 theorem splits_comp_of_splits (j : L →+* F) {f : K[X]} (h : Splits i f) : Splits (j.comp i) f :=
@@ -484,6 +541,7 @@ theorem splits_comp_of_splits (j : L →+* F) {f : K[X]} (h : Splits i f) : Spli
 #align polynomial.splits_comp_of_splits Polynomial.splits_comp_of_splits
 -/
 
+#print Polynomial.splits_iff_card_roots /-
 /-- A polynomial splits if and only if it has as many roots as its degree. -/
 theorem splits_iff_card_roots {p : K[X]} : Splits (RingHom.id K) p ↔ p.roots.card = p.natDegree :=
   by
@@ -495,7 +553,9 @@ theorem splits_iff_card_roots {p : K[X]} : Splits (RingHom.id K) p ↔ p.roots.c
     simp only [RingHom.id_apply, map_id]
     exact (C_leading_coeff_mul_prod_multiset_X_sub_C hroots).symm
 #align polynomial.splits_iff_card_roots Polynomial.splits_iff_card_roots
+-/
 
+#print Polynomial.aeval_root_derivative_of_splits /-
 theorem aeval_root_derivative_of_splits [Algebra K L] {P : K[X]} (hmo : P.Monic)
     (hP : P.Splits (algebraMap K L)) {r : L} (hr : r ∈ (P.map (algebraMap K L)).roots) :
     aeval r P.derivative = (((P.map <| algebraMap K L).roots.eraseₓ r).map fun a => r - a).Prod :=
@@ -506,7 +566,9 @@ theorem aeval_root_derivative_of_splits [Algebra K L] {P : K[X]} (hmo : P.Monic)
   nth_rw 1 [eq_prod_roots_of_monic_of_splits_id hmo hP]
   rw [eval_multiset_prod_X_sub_C_derivative hr]
 #align polynomial.aeval_root_derivative_of_splits Polynomial.aeval_root_derivative_of_splits
+-/
 
+#print Polynomial.prod_roots_eq_coeff_zero_of_monic_of_split /-
 /-- If `P` is a monic polynomial that splits, then `coeff P 0` equals the product of the roots. -/
 theorem prod_roots_eq_coeff_zero_of_monic_of_split {P : K[X]} (hmo : P.Monic)
     (hP : P.Splits (RingHom.id K)) : coeff P 0 = (-1) ^ P.natDegree * P.roots.Prod :=
@@ -522,7 +584,9 @@ theorem prod_roots_eq_coeff_zero_of_monic_of_split {P : K[X]} (hmo : P.Monic)
   rw [Multiset.prod_map_mul, Multiset.map_const, Multiset.prod_replicate, Multiset.map_id',
     splits_iff_card_roots.1 hP]
 #align polynomial.prod_roots_eq_coeff_zero_of_monic_of_split Polynomial.prod_roots_eq_coeff_zero_of_monic_of_split
+-/
 
+#print Polynomial.sum_roots_eq_nextCoeff_of_monic_of_split /-
 /-- If `P` is a monic polynomial that splits, then `P.next_coeff` equals the sum of the roots. -/
 theorem sum_roots_eq_nextCoeff_of_monic_of_split {P : K[X]} (hmo : P.Monic)
     (hP : P.Splits (RingHom.id K)) : P.nextCoeff = -P.roots.Sum :=
@@ -532,6 +596,7 @@ theorem sum_roots_eq_nextCoeff_of_monic_of_split {P : K[X]} (hmo : P.Monic)
   · simp_rw [next_coeff_X_sub_C, Multiset.sum_map_neg']
   · exact monic_X_sub_C a
 #align polynomial.sum_roots_eq_next_coeff_of_monic_of_split Polynomial.sum_roots_eq_nextCoeff_of_monic_of_split
+-/
 
 end Splits
 

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

@@ -103,7 +103,7 @@ theorem splits_of_map_degree_eq_one {f : K[X]} (hf : degree (f.map i) = 1) : Spl
 theorem splits_of_degree_le_one {f : K[X]} (hf : degree f ≤ 1) : Splits i f :=
   if hif : degree (f.map i) ≤ 0 then splits_of_map_eq_C i (degree_le_zero_iff.mp hif)
   else by
-    push_neg  at hif 
+    push_neg at hif 
     rw [← Order.succ_le_iff, ← WithBot.coe_zero, WithBot.succ_coe, Nat.succ_eq_succ] at hif 
     exact splits_of_map_degree_eq_one i (le_antisymm ((degree_map_le i _).trans hf) hif)
 #align polynomial.splits_of_degree_le_one Polynomial.splits_of_degree_le_one
@@ -371,14 +371,14 @@ theorem degree_eq_card_roots {p : K[X]} {i : K →+* L} (p_ne_zero : p ≠ 0) (h
 
 theorem roots_map {f : K[X]} (hf : f.Splits <| RingHom.id K) : (f.map i).roots = f.roots.map i :=
   (roots_map_of_injective_of_card_eq_natDegree i.Injective <| by
-      convert(nat_degree_eq_card_roots hf).symm; rw [map_id]).symm
+      convert (nat_degree_eq_card_roots hf).symm; rw [map_id]).symm
 #align polynomial.roots_map Polynomial.roots_map
 
 theorem image_rootSet [Algebra F K] [Algebra F L] {p : F[X]} (h : p.Splits (algebraMap F K))
     (f : K →ₐ[F] L) : f '' p.rootSet K = p.rootSet L := by
   classical rw [root_set, ← Finset.coe_image, ← Multiset.toFinset_map, ← f.coe_to_ring_hom, ←
-      roots_map (↑f) ((splits_id_iff_splits (algebraMap F K)).mpr h), map_map, f.comp_algebra_map, ←
-      root_set]
+    roots_map (↑f) ((splits_id_iff_splits (algebraMap F K)).mpr h), map_map, f.comp_algebra_map, ←
+    root_set]
 #align polynomial.image_root_set Polynomial.image_rootSet
 
 theorem adjoin_rootSet_eq_range [Algebra F K] [Algebra F L] {p : F[X]}

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

@@ -79,7 +79,7 @@ theorem splits_of_map_eq_C {f : K[X]} {a : L} (h : f.map i = C a) : Splits i f :
           isUnit_iff_degree_eq_zero.2 <| by
             have := congr_arg degree hp
             rw [h, degree_C ha, degree_mul, @eq_comm (WithBot ℕ) 0, Nat.WithBot.add_eq_zero_iff] at
-              this
+              this 
             exact this.1
 #align polynomial.splits_of_map_eq_C Polynomial.splits_of_map_eq_C
 
@@ -93,7 +93,7 @@ theorem splits_of_map_degree_eq_one {f : K[X]} (hf : degree (f.map i) = 1) : Spl
   Or.inr fun g hg ⟨p, hp⟩ => by
     have := congr_arg degree hp <;>
           simp [Nat.WithBot.add_eq_one_iff, hf, @eq_comm (WithBot ℕ) 1,
-            mt is_unit_iff_degree_eq_zero.2 hg.1] at this <;>
+            mt is_unit_iff_degree_eq_zero.2 hg.1] at this  <;>
         clear _fun_match <;>
       tauto
 #align polynomial.splits_of_map_degree_eq_one Polynomial.splits_of_map_degree_eq_one
@@ -103,8 +103,8 @@ theorem splits_of_map_degree_eq_one {f : K[X]} (hf : degree (f.map i) = 1) : Spl
 theorem splits_of_degree_le_one {f : K[X]} (hf : degree f ≤ 1) : Splits i f :=
   if hif : degree (f.map i) ≤ 0 then splits_of_map_eq_C i (degree_le_zero_iff.mp hif)
   else by
-    push_neg  at hif
-    rw [← Order.succ_le_iff, ← WithBot.coe_zero, WithBot.succ_coe, Nat.succ_eq_succ] at hif
+    push_neg  at hif 
+    rw [← Order.succ_le_iff, ← WithBot.coe_zero, WithBot.succ_coe, Nat.succ_eq_succ] at hif 
     exact splits_of_map_degree_eq_one i (le_antisymm ((degree_map_le i _).trans hf) hif)
 #align polynomial.splits_of_degree_le_one Polynomial.splits_of_degree_le_one
 -/
@@ -180,7 +180,7 @@ theorem splits_prod {ι : Type u} {s : ι → K[X]} {t : Finset ι} :
     (∀ j ∈ t, (s j).Splits i) → (∏ x in t, s x).Splits i :=
   by
   refine' Finset.induction_on t (fun _ => splits_one i) fun a t hat ih ht => _
-  rw [Finset.forall_mem_insert] at ht; rw [Finset.prod_insert hat]
+  rw [Finset.forall_mem_insert] at ht ; rw [Finset.prod_insert hat]
   exact splits_mul i ht.1 (ih ht.2)
 #align polynomial.splits_prod Polynomial.splits_prod
 -/
@@ -218,7 +218,7 @@ theorem roots_ne_zero_of_splits' {f : K[X]} (hs : Splits i f) (hf0 : natDegree (
     (f.map i).roots ≠ 0 :=
   let ⟨x, hx⟩ := exists_root_of_splits' i hs fun h => hf0 <| natDegree_eq_of_degree_eq_some h
   fun h => by
-  rw [← eval_map] at hx
+  rw [← eval_map] at hx 
   cases h.subst ((mem_roots _).2 hx); exact ne_zero_of_nat_degree_gt (Nat.pos_of_ne_zero hf0)
 #align polynomial.roots_ne_zero_of_splits' Polynomial.roots_ne_zero_of_splits'
 -/
@@ -242,14 +242,14 @@ theorem natDegree_eq_card_roots' {p : K[X]} {i : K →+* L} (hsplit : Splits i p
   by_cases hp : p.map i = 0
   · rw [hp, nat_degree_zero, roots_zero, Multiset.card_zero]
   obtain ⟨q, he, hd, hr⟩ := exists_prod_multiset_X_sub_C_mul (p.map i)
-  rw [← splits_id_iff_splits, ← he] at hsplit
-  rw [← he] at hp
+  rw [← splits_id_iff_splits, ← he] at hsplit 
+  rw [← he] at hp 
   have hq : q ≠ 0 := fun h => hp (by rw [h, MulZeroClass.mul_zero])
   rw [← hd, add_right_eq_self]
   by_contra
   have h' : (map (RingHom.id L) q).natDegree ≠ 0 := by simp [h]
   have := roots_ne_zero_of_splits' (RingHom.id L) (splits_of_splits_mul' _ _ hsplit).2 h'
-  · rw [map_id] at this; exact this hr
+  · rw [map_id] at this ; exact this hr
   · rw [map_id]; exact mul_ne_zero monic_prod_multiset_X_sub_C.ne_zero hq
 #align polynomial.nat_degree_eq_card_roots' Polynomial.natDegree_eq_card_roots'
 
@@ -313,7 +313,7 @@ theorem splits_prod_iff {ι : Type u} {s : ι → K[X]} {t : Finset ι} :
   refine'
     Finset.induction_on t (fun _ => ⟨fun _ _ h => h.elim, fun _ => splits_one i⟩)
       fun a t hat ih ht => _
-  rw [Finset.forall_mem_insert] at ht⊢
+  rw [Finset.forall_mem_insert] at ht ⊢
   rw [Finset.prod_insert hat, splits_mul_iff i ht.1 (Finset.prod_ne_zero_iff.2 ht.2), ih ht.2]
 #align polynomial.splits_prod_iff Polynomial.splits_prod_iff
 -/
@@ -441,8 +441,8 @@ theorem splits_of_exists_multiset {f : K[X]} {s : Multiset L}
   if hf0 : f = 0 then hf0.symm ▸ splits_zero i
   else
     Or.inr fun p hp hdp => by
-      rw [irreducible_iff_prime] at hp
-      rw [hs, ← Multiset.prod_toList] at hdp
+      rw [irreducible_iff_prime] at hp 
+      rw [hs, ← Multiset.prod_toList] at hdp 
       obtain hd | hd := hp.2.2 _ _ hdp
       · refine' (hp.2.1 <| isUnit_of_dvd_unit hd _).elim
         exact is_unit_C.2 ((leading_coeff_ne_zero.2 hf0).IsUnit.map i)
@@ -477,9 +477,9 @@ theorem splits_iff_exists_multiset {f : K[X]} :
 #print Polynomial.splits_comp_of_splits /-
 theorem splits_comp_of_splits (j : L →+* F) {f : K[X]} (h : Splits i f) : Splits (j.comp i) f :=
   by
-  change i with (RingHom.id _).comp i at h
+  change i with (RingHom.id _).comp i at h 
   rw [← splits_map_iff]
-  rw [← splits_map_iff i] at h
+  rw [← splits_map_iff i] at h 
   exact splits_of_splits_id _ h
 #align polynomial.splits_comp_of_splits Polynomial.splits_comp_of_splits
 -/

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

@@ -374,14 +374,12 @@ theorem roots_map {f : K[X]} (hf : f.Splits <| RingHom.id K) : (f.map i).roots =
       convert(nat_degree_eq_card_roots hf).symm; rw [map_id]).symm
 #align polynomial.roots_map Polynomial.roots_map
 
-#print Polynomial.image_rootSet /-
 theorem image_rootSet [Algebra F K] [Algebra F L] {p : F[X]} (h : p.Splits (algebraMap F K))
     (f : K →ₐ[F] L) : f '' p.rootSet K = p.rootSet L := by
   classical rw [root_set, ← Finset.coe_image, ← Multiset.toFinset_map, ← f.coe_to_ring_hom, ←
       roots_map (↑f) ((splits_id_iff_splits (algebraMap F K)).mpr h), map_map, f.comp_algebra_map, ←
       root_set]
 #align polynomial.image_root_set Polynomial.image_rootSet
--/
 
 theorem adjoin_rootSet_eq_range [Algebra F K] [Algebra F L] {p : F[X]}
     (h : p.Splits (algebraMap F K)) (f : K →ₐ[F] L) :
@@ -498,7 +496,6 @@ theorem splits_iff_card_roots {p : K[X]} : Splits (RingHom.id K) p ↔ p.roots.c
     exact (C_leading_coeff_mul_prod_multiset_X_sub_C hroots).symm
 #align polynomial.splits_iff_card_roots Polynomial.splits_iff_card_roots
 
-#print Polynomial.aeval_root_derivative_of_splits /-
 theorem aeval_root_derivative_of_splits [Algebra K L] {P : K[X]} (hmo : P.Monic)
     (hP : P.Splits (algebraMap K L)) {r : L} (hr : r ∈ (P.map (algebraMap K L)).roots) :
     aeval r P.derivative = (((P.map <| algebraMap K L).roots.eraseₓ r).map fun a => r - a).Prod :=
@@ -509,7 +506,6 @@ theorem aeval_root_derivative_of_splits [Algebra K L] {P : K[X]} (hmo : P.Monic)
   nth_rw 1 [eq_prod_roots_of_monic_of_splits_id hmo hP]
   rw [eval_multiset_prod_X_sub_C_derivative hr]
 #align polynomial.aeval_root_derivative_of_splits Polynomial.aeval_root_derivative_of_splits
--/
 
 /-- If `P` is a monic polynomial that splits, then `coeff P 0` equals the product of the roots. -/
 theorem prod_roots_eq_coeff_zero_of_monic_of_split {P : K[X]} (hmo : P.Monic)

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

@@ -38,7 +38,7 @@ irreducible factors over `L` have degree `1`.
 
 noncomputable section
 
-open Classical BigOperators Polynomial
+open scoped Classical BigOperators Polynomial
 
 universe u v w
 
@@ -99,6 +99,7 @@ theorem splits_of_map_degree_eq_one {f : K[X]} (hf : degree (f.map i) = 1) : Spl
 #align polynomial.splits_of_map_degree_eq_one Polynomial.splits_of_map_degree_eq_one
 -/
 
+#print Polynomial.splits_of_degree_le_one /-
 theorem splits_of_degree_le_one {f : K[X]} (hf : degree f ≤ 1) : Splits i f :=
   if hif : degree (f.map i) ≤ 0 then splits_of_map_eq_C i (degree_le_zero_iff.mp hif)
   else by
@@ -106,6 +107,7 @@ theorem splits_of_degree_le_one {f : K[X]} (hf : degree f ≤ 1) : Splits i f :=
     rw [← Order.succ_le_iff, ← WithBot.coe_zero, WithBot.succ_coe, Nat.succ_eq_succ] at hif
     exact splits_of_map_degree_eq_one i (le_antisymm ((degree_map_le i _).trans hf) hif)
 #align polynomial.splits_of_degree_le_one Polynomial.splits_of_degree_le_one
+-/
 
 #print Polynomial.splits_of_degree_eq_one /-
 theorem splits_of_degree_eq_one {f : K[X]} (hf : degree f = 1) : Splits i f :=

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

@@ -70,12 +70,6 @@ theorem splits_zero : Splits i (0 : K[X]) :=
 #align polynomial.splits_zero Polynomial.splits_zero
 -/
 
-/- warning: polynomial.splits_of_map_eq_C -> Polynomial.splits_of_map_eq_C is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align polynomial.splits_of_map_eq_C Polynomial.splits_of_map_eq_Cₓ'. -/
 theorem splits_of_map_eq_C {f : K[X]} {a : L} (h : f.map i = C a) : Splits i f :=
   if ha : a = 0 then Or.inl (h.trans (ha.symm ▸ C_0))
   else
@@ -89,12 +83,6 @@ theorem splits_of_map_eq_C {f : K[X]} {a : L} (h : f.map i = C a) : Splits i f :
             exact this.1
 #align polynomial.splits_of_map_eq_C Polynomial.splits_of_map_eq_C
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.splits_C Polynomial.splits_Cₓ'. -/
 @[simp]
 theorem splits_C (a : K) : Splits i (C a) :=
   splits_of_map_eq_C i (map_C i)
@@ -111,12 +99,6 @@ theorem splits_of_map_degree_eq_one {f : K[X]} (hf : degree (f.map i) = 1) : Spl
 #align polynomial.splits_of_map_degree_eq_one Polynomial.splits_of_map_degree_eq_one
 -/
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.splits_of_degree_le_one Polynomial.splits_of_degree_le_oneₓ'. -/
 theorem splits_of_degree_le_one {f : K[X]} (hf : degree f ≤ 1) : Splits i f :=
   if hif : degree (f.map i) ≤ 0 then splits_of_map_eq_C i (degree_le_zero_iff.mp hif)
   else by
@@ -177,22 +159,10 @@ theorem splits_one : Splits i 1 :=
 #align polynomial.splits_one Polynomial.splits_one
 -/
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.splits_of_is_unit Polynomial.splits_of_isUnitₓ'. -/
 theorem splits_of_isUnit [IsDomain K] {u : K[X]} (hu : IsUnit u) : u.Splits i :=
   (isUnit_iff.mp hu).choose_spec.2 ▸ splits_C _ _
 #align polynomial.splits_of_is_unit Polynomial.splits_of_isUnit
 
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 theorem splits_X_sub_C {x : K} : (X - C x).Splits i :=
   splits_of_degree_le_one _ <| degree_X_sub_C_le _
 #align polynomial.splits_X_sub_C Polynomial.splits_X_sub_C
@@ -213,24 +183,12 @@ theorem splits_prod {ι : Type u} {s : ι → K[X]} {t : Finset ι} :
 #align polynomial.splits_prod Polynomial.splits_prod
 -/
 
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 theorem splits_pow {f : K[X]} (hf : f.Splits i) (n : ℕ) : (f ^ n).Splits i :=
   by
   rw [← Finset.card_range n, ← Finset.prod_const]
   exact splits_prod i fun j hj => hf
 #align polynomial.splits_pow Polynomial.splits_pow
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.splits_X_pow Polynomial.splits_X_powₓ'. -/
 theorem splits_X_pow (n : ℕ) : (X ^ n).Splits i :=
   splits_pow i (splits_X i) n
 #align polynomial.splits_X_pow Polynomial.splits_X_pow
@@ -241,12 +199,6 @@ theorem splits_id_iff_splits {f : K[X]} : (f.map i).Splits (RingHom.id L) ↔ f.
 #align polynomial.splits_id_iff_splits Polynomial.splits_id_iff_splits
 -/
 
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 theorem exists_root_of_splits' {f : K[X]} (hs : Splits i f) (hf0 : degree (f.map i) ≠ 0) :
     ∃ x, eval₂ i x f = 0 :=
   if hf0' : f.map i = 0 then by simp [eval₂_eq_eval_map, hf0']
@@ -277,23 +229,11 @@ def rootOfSplits' {f : K[X]} (hf : f.Splits i) (hfd : (f.map i).degree ≠ 0) :
 #align polynomial.root_of_splits' Polynomial.rootOfSplits'
 -/
 
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 theorem map_rootOfSplits' {f : K[X]} (hf : f.Splits i) (hfd) :
     f.eval₂ i (rootOfSplits' i hf hfd) = 0 :=
   Classical.choose_spec <| exists_root_of_splits' i hf hfd
 #align polynomial.map_root_of_splits' Polynomial.map_rootOfSplits'
 
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 theorem natDegree_eq_card_roots' {p : K[X]} {i : K →+* L} (hsplit : Splits i p) :
     (p.map i).natDegree = (p.map i).roots.card :=
   by
@@ -311,12 +251,6 @@ theorem natDegree_eq_card_roots' {p : K[X]} {i : K →+* L} (hsplit : Splits i p
   · rw [map_id]; exact mul_ne_zero monic_prod_multiset_X_sub_C.ne_zero hq
 #align polynomial.nat_degree_eq_card_roots' Polynomial.natDegree_eq_card_roots'
 
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 theorem degree_eq_card_roots' {p : K[X]} {i : K →+* L} (p_ne_zero : p.map i ≠ 0)
     (hsplit : Splits i p) : (p.map i).degree = (p.map i).roots.card := by
   rw [degree_eq_nat_degree p_ne_zero, nat_degree_eq_card_roots' hsplit]
@@ -328,24 +262,12 @@ variable [Field K] [Field L] [Field F]
 
 variable (i : K →+* L)
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.splits_iff Polynomial.splits_iffₓ'. -/
 /-- This lemma is for polynomials over a field. -/
 theorem splits_iff (f : K[X]) :
     Splits i f ↔ f = 0 ∨ ∀ {g : L[X]}, Irreducible g → g ∣ f.map i → degree g = 1 := by
   rw [splits, map_eq_zero]
 #align polynomial.splits_iff Polynomial.splits_iff
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.splits.def Polynomial.Splits.defₓ'. -/
 /-- This lemma is for polynomials over a field. -/
 theorem Splits.def {i : K →+* L} {f : K[X]} (h : Splits i f) :
     f = 0 ∨ ∀ {g : L[X]}, Irreducible g → g ∣ f.map i → degree g = 1 :=
@@ -365,23 +287,11 @@ theorem splits_of_splits_of_dvd {f g : K[X]} (hf0 : f ≠ 0) (hf : Splits i f) (
 #align polynomial.splits_of_splits_of_dvd Polynomial.splits_of_splits_of_dvd
 -/
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.splits_of_splits_gcd_left Polynomial.splits_of_splits_gcd_leftₓ'. -/
 theorem splits_of_splits_gcd_left {f g : K[X]} (hf0 : f ≠ 0) (hf : Splits i f) :
     Splits i (EuclideanDomain.gcd f g) :=
   Polynomial.splits_of_splits_of_dvd i hf0 hf (EuclideanDomain.gcd_dvd_left f g)
 #align polynomial.splits_of_splits_gcd_left Polynomial.splits_of_splits_gcd_left
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.splits_of_splits_gcd_right Polynomial.splits_of_splits_gcd_rightₓ'. -/
 theorem splits_of_splits_gcd_right {f g : K[X]} (hg0 : g ≠ 0) (hg : Splits i g) :
     Splits i (EuclideanDomain.gcd f g) :=
   Polynomial.splits_of_splits_of_dvd i hg0 hg (EuclideanDomain.gcd_dvd_right f g)
@@ -406,12 +316,6 @@ theorem splits_prod_iff {ι : Type u} {s : ι → K[X]} {t : Finset ι} :
 #align polynomial.splits_prod_iff Polynomial.splits_prod_iff
 -/
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.degree_eq_one_of_irreducible_of_splits Polynomial.degree_eq_one_of_irreducible_of_splitsₓ'. -/
 theorem degree_eq_one_of_irreducible_of_splits {p : K[X]} (hp : Irreducible p)
     (hp_splits : Splits (RingHom.id K) p) : p.degree = 1 :=
   by
@@ -420,12 +324,6 @@ theorem degree_eq_one_of_irreducible_of_splits {p : K[X]} (hp : Irreducible p)
   · apply hp_splits hp; simp
 #align polynomial.degree_eq_one_of_irreducible_of_splits Polynomial.degree_eq_one_of_irreducible_of_splits
 
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 theorem exists_root_of_splits {f : K[X]} (hs : Splits i f) (hf0 : degree f ≠ 0) :
     ∃ x, eval₂ i x f = 0 :=
   exists_root_of_splits' i hs ((f.degree_map i).symm ▸ hf0)
@@ -454,45 +352,21 @@ theorem rootOfSplits'_eq_rootOfSplits {f : K[X]} (hf : f.Splits i) (hfd) :
 #align polynomial.root_of_splits'_eq_root_of_splits Polynomial.rootOfSplits'_eq_rootOfSplits
 -/
 
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 theorem map_rootOfSplits {f : K[X]} (hf : f.Splits i) (hfd) :
     f.eval₂ i (rootOfSplits i hf hfd) = 0 :=
   map_rootOfSplits' i hf (ne_of_eq_of_ne (degree_map f i) hfd)
 #align polynomial.map_root_of_splits Polynomial.map_rootOfSplits
 
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 theorem natDegree_eq_card_roots {p : K[X]} {i : K →+* L} (hsplit : Splits i p) :
     p.natDegree = (p.map i).roots.card :=
   (natDegree_map i).symm.trans <| natDegree_eq_card_roots' hsplit
 #align polynomial.nat_degree_eq_card_roots Polynomial.natDegree_eq_card_roots
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.degree_eq_card_roots Polynomial.degree_eq_card_rootsₓ'. -/
 theorem degree_eq_card_roots {p : K[X]} {i : K →+* L} (p_ne_zero : p ≠ 0) (hsplit : Splits i p) :
     p.degree = (p.map i).roots.card := by
   rw [degree_eq_nat_degree p_ne_zero, nat_degree_eq_card_roots hsplit]
 #align polynomial.degree_eq_card_roots Polynomial.degree_eq_card_roots
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.roots_map Polynomial.roots_mapₓ'. -/
 theorem roots_map {f : K[X]} (hf : f.Splits <| RingHom.id K) : (f.map i).roots = f.roots.map i :=
   (roots_map_of_injective_of_card_eq_natDegree i.Injective <| by
       convert(nat_degree_eq_card_roots hf).symm; rw [map_id]).symm
@@ -507,12 +381,6 @@ theorem image_rootSet [Algebra F K] [Algebra F L] {p : F[X]} (h : p.Splits (alge
 #align polynomial.image_root_set Polynomial.image_rootSet
 -/
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.adjoin_root_set_eq_range Polynomial.adjoin_rootSet_eq_rangeₓ'. -/
 theorem adjoin_rootSet_eq_range [Algebra F K] [Algebra F L] {p : F[X]}
     (h : p.Splits (algebraMap F K)) (f : K →ₐ[F] L) :
     Algebra.adjoin F (p.rootSet L) = f.range ↔ Algebra.adjoin F (p.rootSet K) = ⊤ :=
@@ -521,9 +389,6 @@ theorem adjoin_rootSet_eq_range [Algebra F K] [Algebra F L] {p : F[X]}
   exact (Subalgebra.map_injective f.to_ring_hom.injective).eq_iff
 #align polynomial.adjoin_root_set_eq_range Polynomial.adjoin_rootSet_eq_range
 
-/- warning: polynomial.eq_prod_roots_of_splits -> Polynomial.eq_prod_roots_of_splits is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.eq_prod_roots_of_splits Polynomial.eq_prod_roots_of_splitsₓ'. -/
 theorem eq_prod_roots_of_splits {p : K[X]} {i : K →+* L} (hsplit : Splits i p) :
     p.map i = C (i p.leadingCoeff) * ((p.map i).roots.map fun a => X - C a).Prod :=
   by
@@ -532,17 +397,11 @@ theorem eq_prod_roots_of_splits {p : K[X]} {i : K →+* L} (hsplit : Splits i p)
   rw [nat_degree_map]; exact (nat_degree_eq_card_roots hsplit).symm
 #align polynomial.eq_prod_roots_of_splits Polynomial.eq_prod_roots_of_splits
 
-/- warning: polynomial.eq_prod_roots_of_splits_id -> Polynomial.eq_prod_roots_of_splits_id is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.eq_prod_roots_of_splits_id Polynomial.eq_prod_roots_of_splits_idₓ'. -/
 theorem eq_prod_roots_of_splits_id {p : K[X]} (hsplit : Splits (RingHom.id K) p) :
     p = C p.leadingCoeff * (p.roots.map fun a => X - C a).Prod := by
   simpa using eq_prod_roots_of_splits hsplit
 #align polynomial.eq_prod_roots_of_splits_id Polynomial.eq_prod_roots_of_splits_id
 
-/- warning: polynomial.eq_prod_roots_of_monic_of_splits_id -> Polynomial.eq_prod_roots_of_monic_of_splits_id is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.eq_prod_roots_of_monic_of_splits_id Polynomial.eq_prod_roots_of_monic_of_splits_idₓ'. -/
 theorem eq_prod_roots_of_monic_of_splits_id {p : K[X]} (m : Monic p)
     (hsplit : Splits (RingHom.id K) p) : p = (p.roots.map fun a => X - C a).Prod :=
   by
@@ -550,9 +409,6 @@ theorem eq_prod_roots_of_monic_of_splits_id {p : K[X]} (m : Monic p)
   simp [m]
 #align polynomial.eq_prod_roots_of_monic_of_splits_id Polynomial.eq_prod_roots_of_monic_of_splits_id
 
-/- warning: polynomial.eq_X_sub_C_of_splits_of_single_root -> Polynomial.eq_X_sub_C_of_splits_of_single_root is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.eq_X_sub_C_of_splits_of_single_root Polynomial.eq_X_sub_C_of_splits_of_single_rootₓ'. -/
 theorem eq_X_sub_C_of_splits_of_single_root {x : K} {h : K[X]} (h_splits : Splits i h)
     (h_roots : (h.map i).roots = {i x}) : h = C h.leadingCoeff * (X - C x) :=
   by
@@ -561,12 +417,6 @@ theorem eq_X_sub_C_of_splits_of_single_root {x : K} {h : K[X]} (h_splits : Split
   simp
 #align polynomial.eq_X_sub_C_of_splits_of_single_root Polynomial.eq_X_sub_C_of_splits_of_single_root
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.mem_lift_of_splits_of_roots_mem_range Polynomial.mem_lift_of_splits_of_roots_mem_rangeₓ'. -/
 theorem mem_lift_of_splits_of_roots_mem_range (R : Type _) [CommRing R] [Algebra R K] {f : K[X]}
     (hs : f.Splits (RingHom.id K)) (hm : f.Monic) (hr : ∀ a ∈ f.roots, a ∈ (algebraMap R K).range) :
     f ∈ Polynomial.lifts (algebraMap R K) :=
@@ -586,9 +436,6 @@ local infixl:50 " ~ᵤ " => Associated
 
 open UniqueFactorizationMonoid Associates
 
-/- warning: polynomial.splits_of_exists_multiset -> Polynomial.splits_of_exists_multiset is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.splits_of_exists_multiset Polynomial.splits_of_exists_multisetₓ'. -/
 theorem splits_of_exists_multiset {f : K[X]} {s : Multiset L}
     (hs : f.map i = C (i f.leadingCoeff) * (s.map fun a : L => X - C a).Prod) : Splits i f :=
   if hf0 : f = 0 then hf0.symm ▸ splits_zero i
@@ -620,9 +467,6 @@ theorem splits_of_splits_id {f : K[X]} : Splits (RingHom.id K) f → Splits i f
 
 end UFD
 
-/- warning: polynomial.splits_iff_exists_multiset -> Polynomial.splits_iff_exists_multiset is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.splits_iff_exists_multiset Polynomial.splits_iff_exists_multisetₓ'. -/
 theorem splits_iff_exists_multiset {f : K[X]} :
     Splits i f ↔
       ∃ s : Multiset L, f.map i = C (i f.leadingCoeff) * (s.map fun a : L => X - C a).Prod :=
@@ -640,12 +484,6 @@ theorem splits_comp_of_splits (j : L →+* F) {f : K[X]} (h : Splits i f) : Spli
 #align polynomial.splits_comp_of_splits Polynomial.splits_comp_of_splits
 -/
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.splits_iff_card_roots Polynomial.splits_iff_card_rootsₓ'. -/
 /-- A polynomial splits if and only if it has as many roots as its degree. -/
 theorem splits_iff_card_roots {p : K[X]} : Splits (RingHom.id K) p ↔ p.roots.card = p.natDegree :=
   by
@@ -671,12 +509,6 @@ theorem aeval_root_derivative_of_splits [Algebra K L] {P : K[X]} (hmo : P.Monic)
 #align polynomial.aeval_root_derivative_of_splits Polynomial.aeval_root_derivative_of_splits
 -/
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.prod_roots_eq_coeff_zero_of_monic_of_split Polynomial.prod_roots_eq_coeff_zero_of_monic_of_splitₓ'. -/
 /-- If `P` is a monic polynomial that splits, then `coeff P 0` equals the product of the roots. -/
 theorem prod_roots_eq_coeff_zero_of_monic_of_split {P : K[X]} (hmo : P.Monic)
     (hP : P.Splits (RingHom.id K)) : coeff P 0 = (-1) ^ P.natDegree * P.roots.Prod :=
@@ -693,12 +525,6 @@ theorem prod_roots_eq_coeff_zero_of_monic_of_split {P : K[X]} (hmo : P.Monic)
     splits_iff_card_roots.1 hP]
 #align polynomial.prod_roots_eq_coeff_zero_of_monic_of_split Polynomial.prod_roots_eq_coeff_zero_of_monic_of_split
 
-/- warning: polynomial.sum_roots_eq_next_coeff_of_monic_of_split -> Polynomial.sum_roots_eq_nextCoeff_of_monic_of_split is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align polynomial.sum_roots_eq_next_coeff_of_monic_of_split Polynomial.sum_roots_eq_nextCoeff_of_monic_of_splitₓ'. -/
 /-- If `P` is a monic polynomial that splits, then `P.next_coeff` equals the sum of the roots. -/
 theorem sum_roots_eq_nextCoeff_of_monic_of_split {P : K[X]} (hmo : P.Monic)
     (hP : P.Splits (RingHom.id K)) : P.nextCoeff = -P.roots.Sum :=

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

@@ -265,8 +265,7 @@ theorem roots_ne_zero_of_splits' {f : K[X]} (hs : Splits i f) (hf0 : natDegree (
   let ⟨x, hx⟩ := exists_root_of_splits' i hs fun h => hf0 <| natDegree_eq_of_degree_eq_some h
   fun h => by
   rw [← eval_map] at hx
-  cases h.subst ((mem_roots _).2 hx)
-  exact ne_zero_of_nat_degree_gt (Nat.pos_of_ne_zero hf0)
+  cases h.subst ((mem_roots _).2 hx); exact ne_zero_of_nat_degree_gt (Nat.pos_of_ne_zero hf0)
 #align polynomial.roots_ne_zero_of_splits' Polynomial.roots_ne_zero_of_splits'
 -/
 
@@ -308,10 +307,8 @@ theorem natDegree_eq_card_roots' {p : K[X]} {i : K →+* L} (hsplit : Splits i p
   by_contra
   have h' : (map (RingHom.id L) q).natDegree ≠ 0 := by simp [h]
   have := roots_ne_zero_of_splits' (RingHom.id L) (splits_of_splits_mul' _ _ hsplit).2 h'
-  · rw [map_id] at this
-    exact this hr
-  · rw [map_id]
-    exact mul_ne_zero monic_prod_multiset_X_sub_C.ne_zero hq
+  · rw [map_id] at this; exact this hr
+  · rw [map_id]; exact mul_ne_zero monic_prod_multiset_X_sub_C.ne_zero hq
 #align polynomial.nat_degree_eq_card_roots' Polynomial.natDegree_eq_card_roots'
 
 /- warning: polynomial.degree_eq_card_roots' -> Polynomial.degree_eq_card_roots' is a dubious translation:
@@ -364,9 +361,7 @@ theorem splits_of_splits_mul {f g : K[X]} (hfg : f * g ≠ 0) (h : Splits i (f *
 
 #print Polynomial.splits_of_splits_of_dvd /-
 theorem splits_of_splits_of_dvd {f g : K[X]} (hf0 : f ≠ 0) (hf : Splits i f) (hgf : g ∣ f) :
-    Splits i g := by
-  obtain ⟨f, rfl⟩ := hgf
-  exact (splits_of_splits_mul i hf0 hf).1
+    Splits i g := by obtain ⟨f, rfl⟩ := hgf; exact (splits_of_splits_mul i hf0 hf).1
 #align polynomial.splits_of_splits_of_dvd Polynomial.splits_of_splits_of_dvd
 -/
 
@@ -421,10 +416,8 @@ theorem degree_eq_one_of_irreducible_of_splits {p : K[X]} (hp : Irreducible p)
     (hp_splits : Splits (RingHom.id K) p) : p.degree = 1 :=
   by
   rcases hp_splits with ⟨⟩
-  · exfalso
-    simp_all
-  · apply hp_splits hp
-    simp
+  · exfalso; simp_all
+  · apply hp_splits hp; simp
 #align polynomial.degree_eq_one_of_irreducible_of_splits Polynomial.degree_eq_one_of_irreducible_of_splits
 
 /- warning: polynomial.exists_root_of_splits -> Polynomial.exists_root_of_splits is a dubious translation:
@@ -501,10 +494,8 @@ but is expected to have type
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) f) -> (Eq.{succ u2} (Multiset.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f)) (Multiset.map.{u1, u2} K L (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) f)))
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_map Polynomial.roots_mapₓ'. -/
 theorem roots_map {f : K[X]} (hf : f.Splits <| RingHom.id K) : (f.map i).roots = f.roots.map i :=
-  (roots_map_of_injective_of_card_eq_natDegree i.Injective <|
-      by
-      convert(nat_degree_eq_card_roots hf).symm
-      rw [map_id]).symm
+  (roots_map_of_injective_of_card_eq_natDegree i.Injective <| by
+      convert(nat_degree_eq_card_roots hf).symm; rw [map_id]).symm
 #align polynomial.roots_map Polynomial.roots_map
 
 #print Polynomial.image_rootSet /-
@@ -659,8 +650,7 @@ Case conversion may be inaccurate. Consider using '#align polynomial.splits_iff_
 theorem splits_iff_card_roots {p : K[X]} : Splits (RingHom.id K) p ↔ p.roots.card = p.natDegree :=
   by
   constructor
-  · intro H
-    rw [nat_degree_eq_card_roots H, map_id]
+  · intro H; rw [nat_degree_eq_card_roots H, map_id]
   · intro hroots
     rw [splits_iff_exists_multiset (RingHom.id K)]
     use p.roots

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

@@ -531,10 +531,7 @@ theorem adjoin_rootSet_eq_range [Algebra F K] [Algebra F L] {p : F[X]}
 #align polynomial.adjoin_root_set_eq_range Polynomial.adjoin_rootSet_eq_range
 
 /- warning: polynomial.eq_prod_roots_of_splits -> Polynomial.eq_prod_roots_of_splits is a dubious translation:
-lean 3 declaration is
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_inst_2)))) (Multiset.map.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (fun (a : L) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (instHSub.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.sub.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.X.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (fun (_x : RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) => L -> (Polynomial.{u2} L (Ring.toSemiring.{u2} 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-but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))} {i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i p) -> (Eq.{succ u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L 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(RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p))) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K 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(Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p))) (Polynomial.mul'.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) 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L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2))))))))) (Polynomial.C.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K 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K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_prod_roots_of_splits Polynomial.eq_prod_roots_of_splitsₓ'. -/
 theorem eq_prod_roots_of_splits {p : K[X]} {i : K →+* L} (hsplit : Splits i p) :
     p.map i = C (i p.leadingCoeff) * ((p.map i).roots.map fun a => X - C a).Prod :=
@@ -545,10 +542,7 @@ theorem eq_prod_roots_of_splits {p : K[X]} {i : K →+* L} (hsplit : Splits i p)
 #align polynomial.eq_prod_roots_of_splits Polynomial.eq_prod_roots_of_splits
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_prod_roots_of_splits_id Polynomial.eq_prod_roots_of_splits_idₓ'. -/
 theorem eq_prod_roots_of_splits_id {p : K[X]} (hsplit : Splits (RingHom.id K) p) :
     p = C p.leadingCoeff * (p.roots.map fun a => X - C a).Prod := by
@@ -556,10 +550,7 @@ theorem eq_prod_roots_of_splits_id {p : K[X]} (hsplit : Splits (RingHom.id K) p)
 #align polynomial.eq_prod_roots_of_splits_id Polynomial.eq_prod_roots_of_splits_id
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_prod_roots_of_monic_of_splits_id Polynomial.eq_prod_roots_of_monic_of_splits_idₓ'. -/
 theorem eq_prod_roots_of_monic_of_splits_id {p : K[X]} (m : Monic p)
     (hsplit : Splits (RingHom.id K) p) : p = (p.roots.map fun a => X - C a).Prod :=
@@ -569,10 +560,7 @@ theorem eq_prod_roots_of_monic_of_splits_id {p : K[X]} (m : Monic p)
 #align polynomial.eq_prod_roots_of_monic_of_splits_id Polynomial.eq_prod_roots_of_monic_of_splits_id
 
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(Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.leadingCoeff.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) h)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K 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(Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) x))))
-but is expected to have type
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(DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L 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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_X_sub_C_of_splits_of_single_root Polynomial.eq_X_sub_C_of_splits_of_single_rootₓ'. -/
 theorem eq_X_sub_C_of_splits_of_single_root {x : K} {h : K[X]} (h_splits : Splits i h)
     (h_roots : (h.map i).roots = {i x}) : h = C h.leadingCoeff * (X - C x) :=
@@ -608,10 +596,7 @@ local infixl:50 " ~ᵤ " => Associated
 open UniqueFactorizationMonoid Associates
 
 /- warning: polynomial.splits_of_exists_multiset -> Polynomial.splits_of_exists_multiset is a dubious translation:
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(Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f))) (Polynomial.mul'.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K 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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.splits_of_exists_multiset Polynomial.splits_of_exists_multisetₓ'. -/
 theorem splits_of_exists_multiset {f : K[X]} {s : Multiset L}
     (hs : f.map i = C (i f.leadingCoeff) * (s.map fun a : L => X - C a).Prod) : Splits i f :=
@@ -645,10 +630,7 @@ theorem splits_of_splits_id {f : K[X]} : Splits (RingHom.id K) f → Splits i f
 end UFD
 
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K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.splits_iff_exists_multiset Polynomial.splits_iff_exists_multisetₓ'. -/
 theorem splits_iff_exists_multiset {f : K[X]} :
     Splits i f ↔

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

@@ -74,7 +74,7 @@ theorem splits_zero : Splits i (0 : K[X]) :=
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))} {a : L}, (Eq.{succ u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i f) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (fun (_x : RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) => L -> (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Polynomial.C.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) a)) -> (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i f)
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {f : Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))} {a : L}, (Eq.{succ u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : L) => Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))))) (Polynomial.C.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a)) -> (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i f)
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {f : Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))} {a : L}, (Eq.{succ u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : L) => Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))))) (Polynomial.C.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a)) -> (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i f)
 Case conversion may be inaccurate. Consider using '#align polynomial.splits_of_map_eq_C Polynomial.splits_of_map_eq_Cₓ'. -/
 theorem splits_of_map_eq_C {f : K[X]} {a : L} (h : f.map i = C a) : Splits i f :=
   if ha : a = 0 then Or.inl (h.trans (ha.symm ▸ C_0))
@@ -93,7 +93,7 @@ theorem splits_of_map_eq_C {f : K[X]} {a : L} (h : f.map i = C a) : Splits i f :
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (a : K), Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) a)
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (a : K), Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)))))))) (Polynomial.C.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) a)
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (a : K), Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)))))))) (Polynomial.C.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) a)
 Case conversion may be inaccurate. Consider using '#align polynomial.splits_C Polynomial.splits_Cₓ'. -/
 @[simp]
 theorem splits_C (a : K) : Splits i (C a) :=
@@ -191,7 +191,7 @@ theorem splits_of_isUnit [IsDomain K] {u : K[X]} (hu : IsUnit u) : u.Splits i :=
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {x : K}, Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (instHSub.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.sub.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.X.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) x))
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {x : K}, Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) x) (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (instHSub.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.sub.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.X.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)))))))) (Polynomial.C.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) x))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {x : K}, Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) x) (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (instHSub.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.sub.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.X.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)))))))) (Polynomial.C.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) x))
 Case conversion may be inaccurate. Consider using '#align polynomial.splits_X_sub_C Polynomial.splits_X_sub_Cₓ'. -/
 theorem splits_X_sub_C {x : K} : (X - C x).Splits i :=
   splits_of_degree_le_one _ <| degree_X_sub_C_le _
@@ -498,7 +498,7 @@ theorem degree_eq_card_roots {p : K[X]} {i : K →+* L} (p_ne_zero : p ≠ 0) (h
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) f) -> (Eq.{succ u2} (Multiset.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i f)) (Multiset.map.{u1, u2} K L (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (fun (_x : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) => K -> L) (RingHom.hasCoeToFun.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) i) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) f)))
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) f) -> (Eq.{succ u2} (Multiset.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f)) (Multiset.map.{u1, u2} K L (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) f)))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) f) -> (Eq.{succ u2} (Multiset.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f)) (Multiset.map.{u1, u2} K L (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) f)))
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_map Polynomial.roots_mapₓ'. -/
 theorem roots_map {f : K[X]} (hf : f.Splits <| RingHom.id K) : (f.map i).roots = f.roots.map i :=
   (roots_map_of_injective_of_card_eq_natDegree i.Injective <|
@@ -534,7 +534,7 @@ theorem adjoin_rootSet_eq_range [Algebra F K] [Algebra F L] {p : F[X]}
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {p : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))} {i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i p) -> (Eq.{succ u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i p) (HMul.hMul.{u2, u2, u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (instHMul.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.mul'.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (fun (_x : RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) => L -> (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Polynomial.C.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (fun (_x : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) => K -> L) (RingHom.hasCoeToFun.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) i (Polynomial.leadingCoeff.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) p))) (Multiset.prod.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (CommRing.toCommMonoid.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)))) (Multiset.map.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (fun (a : L) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (instHSub.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.sub.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.X.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (fun (_x : RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) => L -> (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Polynomial.C.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) a)) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i p))))))
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))} {i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i p) -> (Eq.{succ u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L 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(Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p))) (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p))) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun 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(Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) 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(DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : L) => Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))))) (Polynomial.C.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a)) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p))))))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))} {i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i p) -> (Eq.{succ u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p))) (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p))) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K 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(Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p))) (Polynomial.mul'.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) 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L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2))))))))) (Polynomial.C.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p))) (Multiset.prod.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (CommRing.toCommMonoid.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)))) (Multiset.map.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (fun (a : L) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : L) => Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a) (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (instHSub.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.sub.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.X.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : L) => Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))))) (Polynomial.C.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a)) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_prod_roots_of_splits Polynomial.eq_prod_roots_of_splitsₓ'. -/
 theorem eq_prod_roots_of_splits {p : K[X]} {i : K →+* L} (hsplit : Splits i p) :
     p.map i = C (i p.leadingCoeff) * ((p.map i).roots.map fun a => X - C a).Prod :=
@@ -548,7 +548,7 @@ theorem eq_prod_roots_of_splits {p : K[X]} {i : K →+* L} (hsplit : Splits i p)
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) p) -> (Eq.{succ u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) p (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (instHMul.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.mul'.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.leadingCoeff.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) p)) (Multiset.prod.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.commRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)))) (Multiset.map.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (fun (a : K) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (instHSub.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.X.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) a)) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) p)))))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) p) -> (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) p (HMul.hMul.{u1, u1, u1} ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (instHMul.{u1} ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.mul'.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Multiset.prod.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.commRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)))) (Multiset.map.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (fun (a : K) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) ((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_1)))) a) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) a)) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) p)))))
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) p) -> (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) p (HMul.hMul.{u1, u1, u1} ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (instHMul.{u1} ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.mul'.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Multiset.prod.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.commRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)))) (Multiset.map.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (fun (a : K) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) ((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_1)))) a) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) a)) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) p)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_prod_roots_of_splits_id Polynomial.eq_prod_roots_of_splits_idₓ'. -/
 theorem eq_prod_roots_of_splits_id {p : K[X]} (hsplit : Splits (RingHom.id K) p) :
     p = C p.leadingCoeff * (p.roots.map fun a => X - C a).Prod := by
@@ -559,7 +559,7 @@ theorem eq_prod_roots_of_splits_id {p : K[X]} (hsplit : Splits (RingHom.id K) p)
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Polynomial.Monic.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) p) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) p) -> (Eq.{succ u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) p (Multiset.prod.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.commRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)))) (Multiset.map.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (fun (a : K) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (instHSub.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.X.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) a)) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) p))))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Monic.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) p) -> (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) p (Multiset.prod.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.commRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)))) (Multiset.map.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (fun (a : K) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) ((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_1)))) a) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) a)) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) p))))
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Monic.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) p) -> (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) p (Multiset.prod.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.commRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)))) (Multiset.map.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (fun (a : K) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) ((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_1)))) a) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) a)) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) p))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_prod_roots_of_monic_of_splits_id Polynomial.eq_prod_roots_of_monic_of_splits_idₓ'. -/
 theorem eq_prod_roots_of_monic_of_splits_id {p : K[X]} (m : Monic p)
     (hsplit : Splits (RingHom.id K) p) : p = (p.roots.map fun a => X - C a).Prod :=
@@ -572,7 +572,7 @@ theorem eq_prod_roots_of_monic_of_splits_id {p : K[X]} (m : Monic p)
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {x : K} {h : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i h) -> (Eq.{succ u2} (Multiset.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i h)) (Singleton.singleton.{u2, u2} L (Multiset.{u2} L) (Multiset.hasSingleton.{u2} L) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (fun (_x : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) => K -> L) (RingHom.hasCoeToFun.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) i x))) -> (Eq.{succ u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) h (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (instHMul.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.mul'.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.leadingCoeff.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) h)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (instHSub.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.X.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) x))))
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {x : K} {h : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i h) -> (Eq.{succ u2} (Multiset.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i h)) (Singleton.singleton.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) x) (Multiset.{u2} L) (Multiset.instSingletonMultiset.{u2} L) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i x))) -> (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) h (HMul.hMul.{u1, u1, u1} ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) h)) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (instHMul.{u1} ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) h)) (Polynomial.mul'.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) h)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) ((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_1)))) x) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) x))))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {x : K} {h : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i h) -> (Eq.{succ u2} (Multiset.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i h)) (Singleton.singleton.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) x) (Multiset.{u2} L) (Multiset.instSingletonMultiset.{u2} L) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i x))) -> (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) h (HMul.hMul.{u1, u1, u1} ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) h)) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (instHMul.{u1} ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) h)) (Polynomial.mul'.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) h)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) ((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_1)))) x) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) x))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_X_sub_C_of_splits_of_single_root Polynomial.eq_X_sub_C_of_splits_of_single_rootₓ'. -/
 theorem eq_X_sub_C_of_splits_of_single_root {x : K} {h : K[X]} (h_splits : Splits i h)
     (h_roots : (h.map i).roots = {i x}) : h = C h.leadingCoeff * (X - C x) :=
@@ -611,7 +611,7 @@ open UniqueFactorizationMonoid Associates
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))} {s : Multiset.{u2} L}, (Eq.{succ u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i f) (HMul.hMul.{u2, u2, u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (instHMul.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.mul'.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (fun (_x : RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) => L -> (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Polynomial.C.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (fun (_x : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) => K -> L) (RingHom.hasCoeToFun.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) i (Polynomial.leadingCoeff.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) f))) (Multiset.prod.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (CommRing.toCommMonoid.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)))) (Multiset.map.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (fun (a : L) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (instHSub.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.sub.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.X.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (fun (_x : RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) => L -> (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Polynomial.C.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) a)) s)))) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f)
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))} {s : Multiset.{u2} L}, (Eq.{succ u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L 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(Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))))))) (Polynomial.C.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f))) (Multiset.prod.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (CommRing.toCommMonoid.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)))) (Multiset.map.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (fun (a : L) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : L) => Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a) (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (instHSub.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.sub.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.X.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : L) => Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))))) (Polynomial.C.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a)) s)))) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f)
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))} {s : Multiset.{u2} L}, (Eq.{succ u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f))) (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f))) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f))) (Polynomial.mul'.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K 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(Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun 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(DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))))) (Polynomial.C.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a)) s)))) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f)
 Case conversion may be inaccurate. Consider using '#align polynomial.splits_of_exists_multiset Polynomial.splits_of_exists_multisetₓ'. -/
 theorem splits_of_exists_multiset {f : K[X]} {s : Multiset L}
     (hs : f.map i = C (i f.leadingCoeff) * (s.map fun a : L => X - C a).Prod) : Splits i f :=
@@ -648,7 +648,7 @@ end UFD
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, Iff (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) (Exists.{succ u2} (Multiset.{u2} L) (fun (s : Multiset.{u2} L) => Eq.{succ u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i f) (HMul.hMul.{u2, u2, u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (instHMul.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.mul'.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (fun (_x : RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) => L -> (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Polynomial.C.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (fun (_x : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) => K -> L) (RingHom.hasCoeToFun.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) i (Polynomial.leadingCoeff.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) f))) (Multiset.prod.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (CommRing.toCommMonoid.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)))) (Multiset.map.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (fun (a : L) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (instHSub.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.sub.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.X.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (fun (_x : RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) => L -> (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Polynomial.C.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) a)) s)))))
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, Iff (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) (Exists.{succ u2} (Multiset.{u2} L) (fun (s : Multiset.{u2} L) => Eq.{succ u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f))) (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K 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: K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))))))) (Polynomial.C.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f))) (Multiset.prod.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (CommRing.toCommMonoid.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)))) (Multiset.map.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (fun (a : L) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : L) => Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a) (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (instHSub.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.sub.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.X.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : L) => Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))))) (Polynomial.C.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a)) s)))))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, Iff (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) (Exists.{succ u2} (Multiset.{u2} L) (fun (s : Multiset.{u2} L) => Eq.{succ u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L 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f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun 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(DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))))) (Polynomial.C.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a)) s)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.splits_iff_exists_multiset Polynomial.splits_iff_exists_multisetₓ'. -/
 theorem splits_iff_exists_multiset {f : K[X]} :
     Splits i f ↔

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

@@ -111,7 +111,12 @@ theorem splits_of_map_degree_eq_one {f : K[X]} (hf : degree (f.map i) = 1) : Spl
 #align polynomial.splits_of_map_degree_eq_one Polynomial.splits_of_map_degree_eq_one
 -/
 
-#print Polynomial.splits_of_degree_le_one /-
+/- warning: polynomial.splits_of_degree_le_one -> Polynomial.splits_of_degree_le_one is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _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} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) f) (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.Splits.{u1, u2} K L _inst_1 _inst_2 i f)
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {f : Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _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} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)) f) (OfNat.ofNat.{0} (WithBot.{0} Nat) 1 (One.toOfNat1.{0} (WithBot.{0} Nat) (WithBot.one.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) -> (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i f)
+Case conversion may be inaccurate. Consider using '#align polynomial.splits_of_degree_le_one Polynomial.splits_of_degree_le_oneₓ'. -/
 theorem splits_of_degree_le_one {f : K[X]} (hf : degree f ≤ 1) : Splits i f :=
   if hif : degree (f.map i) ≤ 0 then splits_of_map_eq_C i (degree_le_zero_iff.mp hif)
   else by
@@ -119,7 +124,6 @@ theorem splits_of_degree_le_one {f : K[X]} (hf : degree f ≤ 1) : Splits i f :=
     rw [← Order.succ_le_iff, ← WithBot.coe_zero, WithBot.succ_coe, Nat.succ_eq_succ] at hif
     exact splits_of_map_degree_eq_one i (le_antisymm ((degree_map_le i _).trans hf) hif)
 #align polynomial.splits_of_degree_le_one Polynomial.splits_of_degree_le_one
--/
 
 #print Polynomial.splits_of_degree_eq_one /-
 theorem splits_of_degree_eq_one {f : K[X]} (hf : degree f = 1) : Splits i f :=

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

@@ -331,7 +331,7 @@ variable (i : K →+* L)
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))), Iff (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) (Or (Eq.{succ u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) f (OfNat.ofNat.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.zero.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (forall {g : Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))}, (Irreducible.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Ring.toMonoid.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.ring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) g) -> (Dvd.Dvd.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (semigroupDvd.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (SemigroupWithZero.toSemigroup.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (NonUnitalSemiring.toSemigroupWithZero.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (NonUnitalRing.toNonUnitalSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (NonUnitalCommRing.toNonUnitalRing.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (CommRing.toNonUnitalCommRing.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2))))))))) g (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i f)) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) g) (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 {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))), Iff (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) (Or (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) f (OfNat.ofNat.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.zero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (forall {g : Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))}, (Irreducible.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (MonoidWithZero.toMonoid.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toMonoidWithZero.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) g) -> (Dvd.dvd.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (semigroupDvd.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (SemigroupWithZero.toSemigroup.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalSemiring.toSemigroupWithZero.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (CommRing.toNonUnitalCommRing.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (Field.toCommRing.{u2} L _inst_2)))))))) g (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f)) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) g) (OfNat.ofNat.{0} (WithBot.{0} Nat) 1 (One.toOfNat1.{0} (WithBot.{0} Nat) (WithBot.one.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))))))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))), Iff (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) (Or (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) f (OfNat.ofNat.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.zero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (forall {g : Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))}, (Irreducible.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (MonoidWithZero.toMonoid.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toMonoidWithZero.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) g) -> (Dvd.dvd.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (semigroupDvd.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (SemigroupWithZero.toSemigroup.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalSemiring.toSemigroupWithZero.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (CommRing.toNonUnitalCommRing.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2))))))))) g (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f)) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) g) (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.splits_iff Polynomial.splits_iffₓ'. -/
 /-- This lemma is for polynomials over a field. -/
 theorem splits_iff (f : K[X]) :
@@ -343,7 +343,7 @@ theorem splits_iff (f : K[X]) :
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))} {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) -> (Or (Eq.{succ u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) f (OfNat.ofNat.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.zero.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (forall {g : Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))}, (Irreducible.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Ring.toMonoid.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.ring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) g) -> (Dvd.Dvd.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (semigroupDvd.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (SemigroupWithZero.toSemigroup.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (NonUnitalSemiring.toSemigroupWithZero.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (NonUnitalRing.toNonUnitalSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (NonUnitalCommRing.toNonUnitalRing.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (CommRing.toNonUnitalCommRing.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2))))))))) g (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i f)) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) g) (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 {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))} {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) -> (Or (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) f (OfNat.ofNat.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.zero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (forall {g : Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))}, (Irreducible.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (MonoidWithZero.toMonoid.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toMonoidWithZero.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) g) -> (Dvd.dvd.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (semigroupDvd.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (SemigroupWithZero.toSemigroup.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalSemiring.toSemigroupWithZero.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (CommRing.toNonUnitalCommRing.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (Field.toCommRing.{u2} L _inst_2)))))))) g (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f)) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) g) (OfNat.ofNat.{0} (WithBot.{0} Nat) 1 (One.toOfNat1.{0} (WithBot.{0} Nat) (WithBot.one.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))))))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))} {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) -> (Or (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) f (OfNat.ofNat.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.zero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (forall {g : Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))}, (Irreducible.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (MonoidWithZero.toMonoid.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toMonoidWithZero.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) g) -> (Dvd.dvd.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (semigroupDvd.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (SemigroupWithZero.toSemigroup.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalSemiring.toSemigroupWithZero.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (CommRing.toNonUnitalCommRing.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2))))))))) g (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f)) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) g) (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.splits.def Polynomial.Splits.defₓ'. -/
 /-- This lemma is for polynomials over a field. -/
 theorem Splits.def {i : K →+* L} {f : K[X]} (h : Splits i f) :
@@ -472,7 +472,7 @@ theorem map_rootOfSplits {f : K[X]} (hf : f.Splits i) (hfd) :
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {p : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))} {i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i p) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) p) (coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.orderedCancelAddCommMonoid.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.orderedCancelAddCommMonoid.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u2} L) -> Nat) (AddMonoidHom.hasCoeToFun.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.orderedCancelAddCommMonoid.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i p))))
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))} {i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i p) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p) (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) (fun (_x : Multiset.{u2} L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} L) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} L) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p))))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))} {i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i p) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p) (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) (fun (_x : Multiset.{u2} L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} L) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} L) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p))))
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_eq_card_roots Polynomial.natDegree_eq_card_rootsₓ'. -/
 theorem natDegree_eq_card_roots {p : K[X]} {i : K →+* L} (hsplit : Splits i p) :
     p.natDegree = (p.map i).roots.card :=
@@ -494,7 +494,7 @@ theorem degree_eq_card_roots {p : K[X]} {i : K →+* L} (p_ne_zero : p ≠ 0) (h
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) f) -> (Eq.{succ u2} (Multiset.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i f)) (Multiset.map.{u1, u2} K L (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (fun (_x : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) => K -> L) (RingHom.hasCoeToFun.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) i) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) f)))
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) f) -> (Eq.{succ u2} (Multiset.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f)) (Multiset.map.{u1, u2} K L (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) f)))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) f) -> (Eq.{succ u2} (Multiset.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f)) (Multiset.map.{u1, u2} K L (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) f)))
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_map Polynomial.roots_mapₓ'. -/
 theorem roots_map {f : K[X]} (hf : f.Splits <| RingHom.id K) : (f.map i).roots = f.roots.map i :=
   (roots_map_of_injective_of_card_eq_natDegree i.Injective <|
@@ -530,7 +530,7 @@ theorem adjoin_rootSet_eq_range [Algebra F K] [Algebra F L] {p : F[X]}
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {p : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))} {i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i p) -> (Eq.{succ u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i p) (HMul.hMul.{u2, u2, u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (instHMul.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.mul'.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (fun (_x : RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) => L -> (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Polynomial.C.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (fun (_x : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) => K -> L) (RingHom.hasCoeToFun.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) i (Polynomial.leadingCoeff.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) p))) (Multiset.prod.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (CommRing.toCommMonoid.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)))) (Multiset.map.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (fun (a : L) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (instHSub.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.sub.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.X.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (fun (_x : RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) => L -> (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Polynomial.C.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) a)) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i p))))))
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))} {i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i p) -> (Eq.{succ u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L 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(Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p))) (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p))) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun 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(Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) 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K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p))) (Multiset.prod.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (CommRing.toCommMonoid.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (Field.toCommRing.{u2} L _inst_2))) (Multiset.map.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (fun (a : L) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L 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(Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : L) => Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))))) (Polynomial.C.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a)) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p))))))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))} {i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i p) -> (Eq.{succ u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p))) (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p))) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K 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(Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p))) (Polynomial.mul'.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) 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L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2))))))))) (Polynomial.C.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p))) (Multiset.prod.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (CommRing.toCommMonoid.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)))) (Multiset.map.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (fun (a : L) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : L) => Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a) (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (instHSub.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.sub.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.X.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : L) => Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))))) (Polynomial.C.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a)) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_prod_roots_of_splits Polynomial.eq_prod_roots_of_splitsₓ'. -/
 theorem eq_prod_roots_of_splits {p : K[X]} {i : K →+* L} (hsplit : Splits i p) :
     p.map i = C (i p.leadingCoeff) * ((p.map i).roots.map fun a => X - C a).Prod :=
@@ -544,7 +544,7 @@ theorem eq_prod_roots_of_splits {p : K[X]} {i : K →+* L} (hsplit : Splits i p)
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) p) -> (Eq.{succ u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) p (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (instHMul.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.mul'.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.leadingCoeff.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) p)) (Multiset.prod.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.commRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)))) (Multiset.map.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (fun (a : K) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (instHSub.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.X.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) a)) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) p)))))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) p) -> (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) p (HMul.hMul.{u1, u1, u1} ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (instHMul.{u1} ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.mul'.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Multiset.prod.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.commRing.{u1} K (Field.toCommRing.{u1} K _inst_1))) (Multiset.map.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (fun (a : K) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) ((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_1)))) a) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) a)) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) p)))))
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) p) -> (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) p (HMul.hMul.{u1, u1, u1} ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (instHMul.{u1} ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.mul'.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Multiset.prod.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.commRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)))) (Multiset.map.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (fun (a : K) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) ((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_1)))) a) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) a)) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) p)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_prod_roots_of_splits_id Polynomial.eq_prod_roots_of_splits_idₓ'. -/
 theorem eq_prod_roots_of_splits_id {p : K[X]} (hsplit : Splits (RingHom.id K) p) :
     p = C p.leadingCoeff * (p.roots.map fun a => X - C a).Prod := by
@@ -555,7 +555,7 @@ theorem eq_prod_roots_of_splits_id {p : K[X]} (hsplit : Splits (RingHom.id K) p)
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Polynomial.Monic.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) p) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) p) -> (Eq.{succ u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) p (Multiset.prod.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.commRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)))) (Multiset.map.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (fun (a : K) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (instHSub.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.X.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) a)) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) p))))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Monic.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) p) -> (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) p (Multiset.prod.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.commRing.{u1} K (Field.toCommRing.{u1} K _inst_1))) (Multiset.map.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (fun (a : K) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) ((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_1)))) a) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) a)) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) p))))
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Monic.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) p) -> (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) p (Multiset.prod.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.commRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)))) (Multiset.map.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (fun (a : K) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) ((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_1)))) a) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) a)) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) p))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_prod_roots_of_monic_of_splits_id Polynomial.eq_prod_roots_of_monic_of_splits_idₓ'. -/
 theorem eq_prod_roots_of_monic_of_splits_id {p : K[X]} (m : Monic p)
     (hsplit : Splits (RingHom.id K) p) : p = (p.roots.map fun a => X - C a).Prod :=
@@ -568,7 +568,7 @@ theorem eq_prod_roots_of_monic_of_splits_id {p : K[X]} (m : Monic p)
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {x : K} {h : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i h) -> (Eq.{succ u2} (Multiset.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i h)) (Singleton.singleton.{u2, u2} L (Multiset.{u2} L) (Multiset.hasSingleton.{u2} L) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (fun (_x : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) => K -> L) (RingHom.hasCoeToFun.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) i x))) -> (Eq.{succ u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) h (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (instHMul.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.mul'.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.leadingCoeff.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) h)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (instHSub.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.X.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) x))))
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {x : K} {h : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i h) -> (Eq.{succ u2} (Multiset.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i h)) (Singleton.singleton.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) x) (Multiset.{u2} L) (Multiset.instSingletonMultiset.{u2} L) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i x))) -> (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) h (HMul.hMul.{u1, u1, u1} ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) h)) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (instHMul.{u1} ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) h)) (Polynomial.mul'.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) h)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) ((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_1)))) x) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) x))))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {x : K} {h : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i h) -> (Eq.{succ u2} (Multiset.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i h)) (Singleton.singleton.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) x) (Multiset.{u2} L) (Multiset.instSingletonMultiset.{u2} L) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i x))) -> (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) h (HMul.hMul.{u1, u1, u1} ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) h)) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (instHMul.{u1} ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) h)) (Polynomial.mul'.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) h)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) ((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_1)))) x) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) x))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_X_sub_C_of_splits_of_single_root Polynomial.eq_X_sub_C_of_splits_of_single_rootₓ'. -/
 theorem eq_X_sub_C_of_splits_of_single_root {x : K} {h : K[X]} (h_splits : Splits i h)
     (h_roots : (h.map i).roots = {i x}) : h = C h.leadingCoeff * (X - C x) :=
@@ -582,7 +582,7 @@ theorem eq_X_sub_C_of_splits_of_single_root {x : K} {h : K[X]} (h_splits : Split
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] (R : Type.{u2}) [_inst_4 : CommRing.{u2} R] [_inst_5 : Algebra.{u2, u1} R K (CommRing.toCommSemiring.{u2} R _inst_4) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))] {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) f) -> (Polynomial.Monic.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) f) -> (forall (a : K), (Membership.Mem.{u1, u1} K (Multiset.{u1} K) (Multiset.hasMem.{u1} K) a (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) f)) -> (Membership.Mem.{u1, u1} K (Subring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (SetLike.hasMem.{u1, u1} (Subring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) K (Subring.setLike.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) a (RingHom.range.{u2, u1} R K (CommRing.toRing.{u2} R _inst_4) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (algebraMap.{u2, u1} R K (CommRing.toCommSemiring.{u2} R _inst_4) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_5)))) -> (Membership.Mem.{u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subsemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (SetLike.hasMem.{u1, u1} (Subsemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subsemiring.setLike.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) f (Polynomial.lifts.{u2, u1} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (algebraMap.{u2, u1} R K (CommRing.toCommSemiring.{u2} R _inst_4) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_5)))
 but is expected to have type
-  forall {K : Type.{u2}} [_inst_1 : Field.{u2} K] (R : Type.{u1}) [_inst_4 : CommRing.{u1} R] [_inst_5 : Algebra.{u1, u2} R K (CommRing.toCommSemiring.{u1} R _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))] {f : Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))}, (Polynomial.Splits.{u2, u2} K K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) _inst_1 (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) f) -> (Polynomial.Monic.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) f) -> (forall (a : K), (Membership.mem.{u2, u2} K (Multiset.{u2} K) (Multiset.instMembershipMultiset.{u2} K) a (Polynomial.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) f)) -> (Membership.mem.{u2, u2} K (Subring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1))) (SetLike.instMembership.{u2, u2} (Subring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1))) K (Subring.instSetLikeSubring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))) a (RingHom.range.{u1, u2} R K (CommRing.toRing.{u1} R _inst_4) (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)) (algebraMap.{u1, u2} R K (CommRing.toCommSemiring.{u1} R _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_5)))) -> (Membership.mem.{u2, u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Subsemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))) f (Polynomial.lifts.{u1, u2} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (algebraMap.{u1, u2} R K (CommRing.toCommSemiring.{u1} R _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_5)))
+  forall {K : Type.{u2}} [_inst_1 : Field.{u2} K] (R : Type.{u1}) [_inst_4 : CommRing.{u1} R] [_inst_5 : Algebra.{u1, u2} R K (CommRing.toCommSemiring.{u1} R _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))] {f : Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))}, (Polynomial.Splits.{u2, u2} K K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) _inst_1 (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) f) -> (Polynomial.Monic.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) f) -> (forall (a : K), (Membership.mem.{u2, u2} K (Multiset.{u2} K) (Multiset.instMembershipMultiset.{u2} K) a (Polynomial.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) (Field.isDomain.{u2} K _inst_1) f)) -> (Membership.mem.{u2, u2} K (Subring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1))) (SetLike.instMembership.{u2, u2} (Subring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1))) K (Subring.instSetLikeSubring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))) a (RingHom.range.{u1, u2} R K (CommRing.toRing.{u1} R _inst_4) (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)) (algebraMap.{u1, u2} R K (CommRing.toCommSemiring.{u1} R _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_5)))) -> (Membership.mem.{u2, u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Subsemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))) f (Polynomial.lifts.{u1, u2} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (algebraMap.{u1, u2} R K (CommRing.toCommSemiring.{u1} R _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_5)))
 Case conversion may be inaccurate. Consider using '#align polynomial.mem_lift_of_splits_of_roots_mem_range Polynomial.mem_lift_of_splits_of_roots_mem_rangeₓ'. -/
 theorem mem_lift_of_splits_of_roots_mem_range (R : Type _) [CommRing R] [Algebra R K] {f : K[X]}
     (hs : f.Splits (RingHom.id K)) (hm : f.Monic) (hr : ∀ a ∈ f.roots, a ∈ (algebraMap R K).range) :
@@ -644,7 +644,7 @@ end UFD
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, Iff (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) (Exists.{succ u2} (Multiset.{u2} L) (fun (s : Multiset.{u2} L) => Eq.{succ u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i f) (HMul.hMul.{u2, u2, u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (instHMul.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.mul'.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (fun (_x : RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) => L -> (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Polynomial.C.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (fun (_x : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) => K -> L) (RingHom.hasCoeToFun.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) i (Polynomial.leadingCoeff.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) f))) (Multiset.prod.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (CommRing.toCommMonoid.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)))) (Multiset.map.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (fun (a : L) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (instHSub.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.sub.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.X.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (fun (_x : RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) => L -> (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Polynomial.C.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) a)) s)))))
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, Iff (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) (Exists.{succ u2} (Multiset.{u2} L) (fun (s : Multiset.{u2} L) => Eq.{succ u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f))) (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) 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(Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K 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(Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))))))) (Polynomial.C.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f))) (Multiset.prod.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (CommRing.toCommMonoid.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (Field.toCommRing.{u2} L _inst_2))) (Multiset.map.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (fun (a : L) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : L) => Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a) (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (instHSub.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.sub.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.X.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : L) => Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))))) (Polynomial.C.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a)) s)))))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, Iff (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) (Exists.{succ u2} (Multiset.{u2} L) (fun (s : Multiset.{u2} L) => Eq.{succ u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f))) (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K 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(DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))))))) (Polynomial.C.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f))) (Multiset.prod.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (CommRing.toCommMonoid.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)))) (Multiset.map.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (fun (a : L) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : L) => Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a) (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (instHSub.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.sub.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.X.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : L) => Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))))) (Polynomial.C.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a)) s)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.splits_iff_exists_multiset Polynomial.splits_iff_exists_multisetₓ'. -/
 theorem splits_iff_exists_multiset {f : K[X]} :
     Splits i f ↔
@@ -667,7 +667,7 @@ theorem splits_comp_of_splits (j : L →+* F) {f : K[X]} (h : Splits i f) : Spli
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, Iff (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) p) (Eq.{1} Nat (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.orderedCancelAddCommMonoid.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.orderedCancelAddCommMonoid.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} K) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.orderedCancelAddCommMonoid.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} K) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) p)) (Polynomial.natDegree.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) p))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, Iff (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) p) (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} K) => Nat) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) p)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} K) (fun (_x : Multiset.{u1} K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} K) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} K) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} K) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} K) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) p)) (Polynomial.natDegree.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p))
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, Iff (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) p) (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} K) => Nat) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) p)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} K) (fun (_x : Multiset.{u1} K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} K) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} K) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} K) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} K) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) p)) (Polynomial.natDegree.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.splits_iff_card_roots Polynomial.splits_iff_card_rootsₓ'. -/
 /-- A polynomial splits if and only if it has as many roots as its degree. -/
 theorem splits_iff_card_roots {p : K[X]} : Splits (RingHom.id K) p ↔ p.roots.card = p.natDegree :=
@@ -699,7 +699,7 @@ theorem aeval_root_derivative_of_splits [Algebra K L] {P : K[X]} (hmo : P.Monic)
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {P : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Polynomial.Monic.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) P) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) P) -> (Eq.{succ u1} K (Polynomial.coeff.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) P (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (AddGroupWithOne.toAddGroup.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) (Polynomial.natDegree.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) P)) (Multiset.prod.{u1} K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) P))))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {P : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Monic.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) P) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) P) -> (Eq.{succ u1} K (Polynomial.coeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) P (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Polynomial.natDegree.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) P)) (Multiset.prod.{u1} K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) P))))
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {P : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Monic.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) P) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) P) -> (Eq.{succ u1} K (Polynomial.coeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) P (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Polynomial.natDegree.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) P)) (Multiset.prod.{u1} K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) P))))
 Case conversion may be inaccurate. Consider using '#align polynomial.prod_roots_eq_coeff_zero_of_monic_of_split Polynomial.prod_roots_eq_coeff_zero_of_monic_of_splitₓ'. -/
 /-- If `P` is a monic polynomial that splits, then `coeff P 0` equals the product of the roots. -/
 theorem prod_roots_eq_coeff_zero_of_monic_of_split {P : K[X]} (hmo : P.Monic)
@@ -721,7 +721,7 @@ theorem prod_roots_eq_coeff_zero_of_monic_of_split {P : K[X]} (hmo : P.Monic)
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {P : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Polynomial.Monic.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) P) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) P) -> (Eq.{succ u1} K (Polynomial.nextCoeff.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) P) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (AddGroupWithOne.toAddGroup.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Multiset.sum.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) P))))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {P : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Monic.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) P) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) P) -> (Eq.{succ u1} K (Polynomial.nextCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) P) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Multiset.sum.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) P))))
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {P : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Monic.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) P) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) P) -> (Eq.{succ u1} K (Polynomial.nextCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) P) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Multiset.sum.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) P))))
 Case conversion may be inaccurate. Consider using '#align polynomial.sum_roots_eq_next_coeff_of_monic_of_split Polynomial.sum_roots_eq_nextCoeff_of_monic_of_splitₓ'. -/
 /-- If `P` is a monic polynomial that splits, then `P.next_coeff` equals the sum of the roots. -/
 theorem sum_roots_eq_nextCoeff_of_monic_of_split {P : K[X]} (hmo : P.Monic)

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

@@ -74,7 +74,7 @@ theorem splits_zero : Splits i (0 : K[X]) :=
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))} {a : L}, (Eq.{succ u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i f) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (fun (_x : RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) => L -> (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Polynomial.C.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) a)) -> (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i f)
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))} {a : L}, (Eq.{succ u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : L) => Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))))) (Polynomial.C.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a)) -> (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i f)
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {f : Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))} {a : L}, (Eq.{succ u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : L) => Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))))) (Polynomial.C.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a)) -> (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i f)
 Case conversion may be inaccurate. Consider using '#align polynomial.splits_of_map_eq_C Polynomial.splits_of_map_eq_Cₓ'. -/
 theorem splits_of_map_eq_C {f : K[X]} {a : L} (h : f.map i = C a) : Splits i f :=
   if ha : a = 0 then Or.inl (h.trans (ha.symm ▸ C_0))
@@ -93,7 +93,7 @@ theorem splits_of_map_eq_C {f : K[X]} {a : L} (h : f.map i = C a) : Splits i f :
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (a : K), Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) a)
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (a : K), Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)))))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) a)
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (a : K), Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)))))))) (Polynomial.C.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) a)
 Case conversion may be inaccurate. Consider using '#align polynomial.splits_C Polynomial.splits_Cₓ'. -/
 @[simp]
 theorem splits_C (a : K) : Splits i (C a) :=
@@ -177,7 +177,7 @@ theorem splits_one : Splits i 1 :=
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) [_inst_4 : IsDomain.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))] {u : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))}, (IsUnit.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.ring.{u1} K (CommRing.toRing.{u1} K _inst_1))) u) -> (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i u)
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) [_inst_4 : IsDomain.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))] {u : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))}, (IsUnit.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) u) -> (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i u)
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) [_inst_4 : IsDomain.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))] {u : Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))}, (IsUnit.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) u) -> (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i u)
 Case conversion may be inaccurate. Consider using '#align polynomial.splits_of_is_unit Polynomial.splits_of_isUnitₓ'. -/
 theorem splits_of_isUnit [IsDomain K] {u : K[X]} (hu : IsUnit u) : u.Splits i :=
   (isUnit_iff.mp hu).choose_spec.2 ▸ splits_C _ _
@@ -187,7 +187,7 @@ theorem splits_of_isUnit [IsDomain K] {u : K[X]} (hu : IsUnit u) : u.Splits i :=
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {x : K}, Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (instHSub.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.sub.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.X.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) x))
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {x : K}, Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) x) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (instHSub.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.sub.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.X.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)))))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) x))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {x : K}, Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) x) (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (instHSub.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.sub.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.X.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)))))))) (Polynomial.C.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) x))
 Case conversion may be inaccurate. Consider using '#align polynomial.splits_X_sub_C Polynomial.splits_X_sub_Cₓ'. -/
 theorem splits_X_sub_C {x : K} : (X - C x).Splits i :=
   splits_of_degree_le_one _ <| degree_X_sub_C_le _
@@ -213,7 +213,7 @@ theorem splits_prod {ι : Type u} {s : ι → K[X]} {t : Finset ι} :
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))}, (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i f) -> (forall (n : Nat), Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) Nat (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.ring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) f n))
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))}, (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i f) -> (forall (n : Nat), Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) Nat (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))))) f n))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {f : Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))}, (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i f) -> (forall (n : Nat), Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) Nat (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))))) f n))
 Case conversion may be inaccurate. Consider using '#align polynomial.splits_pow Polynomial.splits_powₓ'. -/
 theorem splits_pow {f : K[X]} (hf : f.Splits i) (n : ℕ) : (f ^ n).Splits i :=
   by
@@ -225,7 +225,7 @@ theorem splits_pow {f : K[X]} (hf : f.Splits i) (n : ℕ) : (f ^ n).Splits i :=
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (n : Nat), Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) Nat (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.ring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) (Polynomial.X.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) n)
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (n : Nat), Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) Nat (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))))) (Polynomial.X.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) n)
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (n : Nat), Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) Nat (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))))) (Polynomial.X.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) n)
 Case conversion may be inaccurate. Consider using '#align polynomial.splits_X_pow Polynomial.splits_X_powₓ'. -/
 theorem splits_X_pow (n : ℕ) : (X ^ n).Splits i :=
   splits_pow i (splits_X i) n
@@ -241,7 +241,7 @@ theorem splits_id_iff_splits {f : K[X]} : (f.map i).Splits (RingHom.id L) ↔ f.
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))}, (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i f) -> (Ne.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i f)) (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))))) -> (Exists.{succ u2} L (fun (x : L) => Eq.{succ u2} L (Polynomial.eval₂.{u1, u2} K L (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i x f) (OfNat.ofNat.{u2} L 0 (OfNat.mk.{u2} L 0 (Zero.zero.{u2} L (MulZeroClass.toHasZero.{u2} L (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))))))
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))}, (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i f) -> (Ne.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f)) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) -> (Exists.{succ u2} L (fun (x : L) => Eq.{succ u2} L (Polynomial.eval₂.{u1, u2} K L (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i x f) (OfNat.ofNat.{u2} L 0 (Zero.toOfNat0.{u2} L (CommMonoidWithZero.toZero.{u2} L (CommGroupWithZero.toCommMonoidWithZero.{u2} L (Semifield.toCommGroupWithZero.{u2} L (Field.toSemifield.{u2} L _inst_2))))))))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {f : Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))}, (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i f) -> (Ne.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (Polynomial.map.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f)) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) -> (Exists.{succ u2} L (fun (x : L) => Eq.{succ u2} L (Polynomial.eval₂.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i x f) (OfNat.ofNat.{u2} L 0 (Zero.toOfNat0.{u2} L (CommMonoidWithZero.toZero.{u2} L (CommGroupWithZero.toCommMonoidWithZero.{u2} L (Semifield.toCommGroupWithZero.{u2} L (Field.toSemifield.{u2} L _inst_2))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.exists_root_of_splits' Polynomial.exists_root_of_splits'ₓ'. -/
 theorem exists_root_of_splits' {f : K[X]} (hs : Splits i f) (hf0 : degree (f.map i) ≠ 0) :
     ∃ x, eval₂ i x f = 0 :=
@@ -278,7 +278,7 @@ def rootOfSplits' {f : K[X]} (hf : f.Splits i) (hfd : (f.map i).degree ≠ 0) :
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))} (hf : Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i f) (hfd : Ne.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i f)) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero))))), Eq.{succ u2} L (Polynomial.eval₂.{u1, u2} K L (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i (Polynomial.rootOfSplits'.{u1, u2} K L _inst_1 _inst_2 i f hf hfd) f) (OfNat.ofNat.{u2} L 0 (OfNat.mk.{u2} L 0 (Zero.zero.{u2} L (MulZeroClass.toHasZero.{u2} L (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))))
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))} (hf : Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i f) (hfd : Ne.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f)) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))), Eq.{succ u2} L (Polynomial.eval₂.{u1, u2} K L (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i (Polynomial.rootOfSplits'.{u1, u2} K L _inst_1 _inst_2 i f hf hfd) f) (OfNat.ofNat.{u2} L 0 (Zero.toOfNat0.{u2} L (CommMonoidWithZero.toZero.{u2} L (CommGroupWithZero.toCommMonoidWithZero.{u2} L (Semifield.toCommGroupWithZero.{u2} L (Field.toSemifield.{u2} L _inst_2))))))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {f : Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))} (hf : Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i f) (hfd : Ne.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (Polynomial.map.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f)) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))), Eq.{succ u2} L (Polynomial.eval₂.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i (Polynomial.rootOfSplits'.{u1, u2} K L _inst_1 _inst_2 i f hf hfd) f) (OfNat.ofNat.{u2} L 0 (Zero.toOfNat0.{u2} L (CommMonoidWithZero.toZero.{u2} L (CommGroupWithZero.toCommMonoidWithZero.{u2} L (Semifield.toCommGroupWithZero.{u2} L (Field.toSemifield.{u2} L _inst_2))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_root_of_splits' Polynomial.map_rootOfSplits'ₓ'. -/
 theorem map_rootOfSplits' {f : K[X]} (hf : f.Splits i) (hfd) :
     f.eval₂ i (rootOfSplits' i hf hfd) = 0 :=
@@ -289,7 +289,7 @@ theorem map_rootOfSplits' {f : K[X]} (hf : f.Splits i) (hfd) :
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] {p : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))} {i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))}, (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i p) -> (Eq.{1} Nat (Polynomial.natDegree.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i p)) (coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.orderedCancelAddCommMonoid.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.orderedCancelAddCommMonoid.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u2} L) -> Nat) (AddMonoidHom.hasCoeToFun.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.orderedCancelAddCommMonoid.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i p))))
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] {p : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))} {i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))}, (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i p) -> (Eq.{1} Nat (Polynomial.natDegree.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p)) (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) (fun (_x : Multiset.{u2} L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} L) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} L) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p))))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] {p : Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))} {i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))}, (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i p) -> (Eq.{1} Nat (Polynomial.natDegree.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (Polynomial.map.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p)) (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) (fun (_x : Multiset.{u2} L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} L) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} L) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p))))
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_eq_card_roots' Polynomial.natDegree_eq_card_roots'ₓ'. -/
 theorem natDegree_eq_card_roots' {p : K[X]} {i : K →+* L} (hsplit : Splits i p) :
     (p.map i).natDegree = (p.map i).roots.card :=
@@ -314,7 +314,7 @@ theorem natDegree_eq_card_roots' {p : K[X]} {i : K →+* L} (hsplit : Splits i p
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] {p : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))} {i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))}, (Ne.{succ u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i p) (OfNat.ofNat.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) 0 (OfNat.mk.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) 0 (Zero.zero.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.zero.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))))) -> (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i p) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i p)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.orderedCancelAddCommMonoid.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.orderedCancelAddCommMonoid.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u2} L) -> Nat) (AddMonoidHom.hasCoeToFun.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.orderedCancelAddCommMonoid.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i p)))))
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] {p : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))} {i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))}, (Ne.{succ u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p) (OfNat.ofNat.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.zero.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) -> (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i p) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) (fun (_x : Multiset.{u2} L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} L) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} L) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p)))))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] {p : Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))} {i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))}, (Ne.{succ u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p) (OfNat.ofNat.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.zero.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) -> (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i p) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (Polynomial.map.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) (fun (_x : Multiset.{u2} L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} L) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} L) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.degree_eq_card_roots' Polynomial.degree_eq_card_roots'ₓ'. -/
 theorem degree_eq_card_roots' {p : K[X]} {i : K →+* L} (p_ne_zero : p.map i ≠ 0)
     (hsplit : Splits i p) : (p.map i).degree = (p.map i).roots.card := by
@@ -331,7 +331,7 @@ variable (i : K →+* L)
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))), Iff (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) (Or (Eq.{succ u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) f (OfNat.ofNat.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.zero.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (forall {g : Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))}, (Irreducible.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Ring.toMonoid.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.ring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) g) -> (Dvd.Dvd.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (semigroupDvd.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (SemigroupWithZero.toSemigroup.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (NonUnitalSemiring.toSemigroupWithZero.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (NonUnitalRing.toNonUnitalSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (NonUnitalCommRing.toNonUnitalRing.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (CommRing.toNonUnitalCommRing.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2))))))))) g (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i f)) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) g) (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 {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))), Iff (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) (Or (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) f (OfNat.ofNat.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.zero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (forall {g : Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))}, (Irreducible.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (MonoidWithZero.toMonoid.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toMonoidWithZero.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) g) -> (Dvd.dvd.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (semigroupDvd.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (SemigroupWithZero.toSemigroup.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalSemiring.toSemigroupWithZero.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalRing.toNonUnitalSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalCommRing.toNonUnitalRing.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (CommRing.toNonUnitalCommRing.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} L _inst_2)))))))) g (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f)) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) g) (OfNat.ofNat.{0} (WithBot.{0} Nat) 1 (One.toOfNat1.{0} (WithBot.{0} Nat) (WithBot.one.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))))))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))), Iff (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) (Or (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) f (OfNat.ofNat.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.zero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (forall {g : Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))}, (Irreducible.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (MonoidWithZero.toMonoid.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toMonoidWithZero.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) g) -> (Dvd.dvd.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (semigroupDvd.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (SemigroupWithZero.toSemigroup.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalSemiring.toSemigroupWithZero.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (CommRing.toNonUnitalCommRing.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (Field.toCommRing.{u2} L _inst_2)))))))) g (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f)) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) g) (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.splits_iff Polynomial.splits_iffₓ'. -/
 /-- This lemma is for polynomials over a field. -/
 theorem splits_iff (f : K[X]) :
@@ -343,7 +343,7 @@ theorem splits_iff (f : K[X]) :
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))} {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) -> (Or (Eq.{succ u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) f (OfNat.ofNat.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.zero.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (forall {g : Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))}, (Irreducible.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Ring.toMonoid.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.ring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) g) -> (Dvd.Dvd.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (semigroupDvd.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (SemigroupWithZero.toSemigroup.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (NonUnitalSemiring.toSemigroupWithZero.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (NonUnitalRing.toNonUnitalSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (NonUnitalCommRing.toNonUnitalRing.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (CommRing.toNonUnitalCommRing.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2))))))))) g (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i f)) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) g) (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 {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))} {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) -> (Or (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) f (OfNat.ofNat.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.zero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (forall {g : Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))}, (Irreducible.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (MonoidWithZero.toMonoid.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toMonoidWithZero.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) g) -> (Dvd.dvd.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (semigroupDvd.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (SemigroupWithZero.toSemigroup.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalSemiring.toSemigroupWithZero.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalRing.toNonUnitalSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalCommRing.toNonUnitalRing.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (CommRing.toNonUnitalCommRing.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} L _inst_2)))))))) g (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f)) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) g) (OfNat.ofNat.{0} (WithBot.{0} Nat) 1 (One.toOfNat1.{0} (WithBot.{0} Nat) (WithBot.one.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))))))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))} {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) -> (Or (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) f (OfNat.ofNat.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.zero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (forall {g : Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))}, (Irreducible.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (MonoidWithZero.toMonoid.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toMonoidWithZero.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) g) -> (Dvd.dvd.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (semigroupDvd.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (SemigroupWithZero.toSemigroup.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalSemiring.toSemigroupWithZero.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (CommRing.toNonUnitalCommRing.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (Field.toCommRing.{u2} L _inst_2)))))))) g (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f)) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) g) (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.splits.def Polynomial.Splits.defₓ'. -/
 /-- This lemma is for polynomials over a field. -/
 theorem Splits.def {i : K →+* L} {f : K[X]} (h : Splits i f) :
@@ -370,7 +370,7 @@ theorem splits_of_splits_of_dvd {f g : K[X]} (hf0 : f ≠ 0) (hf : Splits i f) (
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))} {g : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) f (OfNat.ofNat.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.zero.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i (EuclideanDomain.gcd.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) (Polynomial.euclideanDomain.{u1} K _inst_1) (fun (a : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) (b : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) a b)) f g))
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))} {g : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) f (OfNat.ofNat.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.zero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i (EuclideanDomain.gcd.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} K _inst_1) (fun (a : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) (b : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) a b)) f g))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))} {g : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) f (OfNat.ofNat.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.zero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i (EuclideanDomain.gcd.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} K _inst_1) (fun (a : Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) (b : Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) a b)) f g))
 Case conversion may be inaccurate. Consider using '#align polynomial.splits_of_splits_gcd_left Polynomial.splits_of_splits_gcd_leftₓ'. -/
 theorem splits_of_splits_gcd_left {f g : K[X]} (hf0 : f ≠ 0) (hf : Splits i f) :
     Splits i (EuclideanDomain.gcd f g) :=
@@ -381,7 +381,7 @@ theorem splits_of_splits_gcd_left {f g : K[X]} (hf0 : f ≠ 0) (hf : Splits i f)
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))} {g : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) g (OfNat.ofNat.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.zero.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i g) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i (EuclideanDomain.gcd.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) (Polynomial.euclideanDomain.{u1} K _inst_1) (fun (a : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) (b : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) a b)) f g))
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))} {g : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) g (OfNat.ofNat.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.zero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i g) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i (EuclideanDomain.gcd.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} K _inst_1) (fun (a : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) (b : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) a b)) f g))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))} {g : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) g (OfNat.ofNat.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.zero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i g) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i (EuclideanDomain.gcd.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} K _inst_1) (fun (a : Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) (b : Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) a b)) f g))
 Case conversion may be inaccurate. Consider using '#align polynomial.splits_of_splits_gcd_right Polynomial.splits_of_splits_gcd_rightₓ'. -/
 theorem splits_of_splits_gcd_right {f g : K[X]} (hg0 : g ≠ 0) (hg : Splits i g) :
     Splits i (EuclideanDomain.gcd f g) :=
@@ -411,7 +411,7 @@ theorem splits_prod_iff {ι : Type u} {s : ι → K[X]} {t : Finset ι} :
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.ring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) p) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) p) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _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 {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) p) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) p) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _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 {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) p) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) p) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _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_splits Polynomial.degree_eq_one_of_irreducible_of_splitsₓ'. -/
 theorem degree_eq_one_of_irreducible_of_splits {p : K[X]} (hp : Irreducible p)
     (hp_splits : Splits (RingHom.id K) p) : p.degree = 1 :=
@@ -427,7 +427,7 @@ theorem degree_eq_one_of_irreducible_of_splits {p : K[X]} (hp : Irreducible p)
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) -> (Ne.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) f) (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))))) -> (Exists.{succ u2} L (fun (x : L) => Eq.{succ u2} L (Polynomial.eval₂.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i x f) (OfNat.ofNat.{u2} L 0 (OfNat.mk.{u2} L 0 (Zero.zero.{u2} L (MulZeroClass.toHasZero.{u2} L (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))))))
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) -> (Ne.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) -> (Exists.{succ u2} L (fun (x : L) => Eq.{succ u2} L (Polynomial.eval₂.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i x f) (OfNat.ofNat.{u2} L 0 (Zero.toOfNat0.{u2} L (CommMonoidWithZero.toZero.{u2} L (CommGroupWithZero.toCommMonoidWithZero.{u2} L (Semifield.toCommGroupWithZero.{u2} L (Field.toSemifield.{u2} L _inst_2))))))))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) -> (Ne.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) -> (Exists.{succ u2} L (fun (x : L) => Eq.{succ u2} L (Polynomial.eval₂.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i x f) (OfNat.ofNat.{u2} L 0 (Zero.toOfNat0.{u2} L (CommMonoidWithZero.toZero.{u2} L (CommGroupWithZero.toCommMonoidWithZero.{u2} L (Semifield.toCommGroupWithZero.{u2} L (Field.toSemifield.{u2} L _inst_2))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.exists_root_of_splits Polynomial.exists_root_of_splitsₓ'. -/
 theorem exists_root_of_splits {f : K[X]} (hs : Splits i f) (hf0 : degree f ≠ 0) :
     ∃ x, eval₂ i x f = 0 :=
@@ -461,7 +461,7 @@ theorem rootOfSplits'_eq_rootOfSplits {f : K[X]} (hf : f.Splits i) (hfd) :
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))} (hf : Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) (hfd : Ne.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) f) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero))))), Eq.{succ u2} L (Polynomial.eval₂.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i (Polynomial.rootOfSplits.{u1, u2} K L _inst_1 _inst_2 i f hf hfd) f) (OfNat.ofNat.{u2} L 0 (OfNat.mk.{u2} L 0 (Zero.zero.{u2} L (MulZeroClass.toHasZero.{u2} L (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))))
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))} (hf : Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) (hfd : Ne.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))), Eq.{succ u2} L (Polynomial.eval₂.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i (Polynomial.rootOfSplits.{u1, u2} K L _inst_1 _inst_2 i f hf hfd) f) (OfNat.ofNat.{u2} L 0 (Zero.toOfNat0.{u2} L (CommMonoidWithZero.toZero.{u2} L (CommGroupWithZero.toCommMonoidWithZero.{u2} L (Semifield.toCommGroupWithZero.{u2} L (Field.toSemifield.{u2} L _inst_2))))))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))} (hf : Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) (hfd : Ne.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))), Eq.{succ u2} L (Polynomial.eval₂.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i (Polynomial.rootOfSplits.{u1, u2} K L _inst_1 _inst_2 i f hf hfd) f) (OfNat.ofNat.{u2} L 0 (Zero.toOfNat0.{u2} L (CommMonoidWithZero.toZero.{u2} L (CommGroupWithZero.toCommMonoidWithZero.{u2} L (Semifield.toCommGroupWithZero.{u2} L (Field.toSemifield.{u2} L _inst_2))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_root_of_splits Polynomial.map_rootOfSplitsₓ'. -/
 theorem map_rootOfSplits {f : K[X]} (hf : f.Splits i) (hfd) :
     f.eval₂ i (rootOfSplits i hf hfd) = 0 :=
@@ -472,7 +472,7 @@ theorem map_rootOfSplits {f : K[X]} (hf : f.Splits i) (hfd) :
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {p : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))} {i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i p) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) p) (coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.orderedCancelAddCommMonoid.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.orderedCancelAddCommMonoid.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u2} L) -> Nat) (AddMonoidHom.hasCoeToFun.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.orderedCancelAddCommMonoid.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i p))))
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))} {i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i p) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p) (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) (fun (_x : Multiset.{u2} L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} L) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} L) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p))))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))} {i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i p) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p) (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) (fun (_x : Multiset.{u2} L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} L) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} L) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p))))
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_eq_card_roots Polynomial.natDegree_eq_card_rootsₓ'. -/
 theorem natDegree_eq_card_roots {p : K[X]} {i : K →+* L} (hsplit : Splits i p) :
     p.natDegree = (p.map i).roots.card :=
@@ -483,7 +483,7 @@ theorem natDegree_eq_card_roots {p : K[X]} {i : K →+* L} (hsplit : Splits i p)
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {p : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))} {i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))}, (Ne.{succ u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) p (OfNat.ofNat.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.zero.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i p) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) p) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.orderedCancelAddCommMonoid.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.orderedCancelAddCommMonoid.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u2} L) -> Nat) (AddMonoidHom.hasCoeToFun.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.orderedCancelAddCommMonoid.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i p)))))
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))} {i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))}, (Ne.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) p (OfNat.ofNat.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.zero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i p) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) (fun (_x : Multiset.{u2} L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} L) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} L) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p)))))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))} {i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))}, (Ne.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) p (OfNat.ofNat.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.zero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i p) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) (fun (_x : Multiset.{u2} L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} L) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} L) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.degree_eq_card_roots Polynomial.degree_eq_card_rootsₓ'. -/
 theorem degree_eq_card_roots {p : K[X]} {i : K →+* L} (p_ne_zero : p ≠ 0) (hsplit : Splits i p) :
     p.degree = (p.map i).roots.card := by
@@ -494,7 +494,7 @@ theorem degree_eq_card_roots {p : K[X]} {i : K →+* L} (p_ne_zero : p ≠ 0) (h
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) f) -> (Eq.{succ u2} (Multiset.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i f)) (Multiset.map.{u1, u2} K L (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (fun (_x : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) => K -> L) (RingHom.hasCoeToFun.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) i) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) f)))
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) f) -> (Eq.{succ u2} (Multiset.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f)) (Multiset.map.{u1, u2} K L (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))))) i) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) f)))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) f) -> (Eq.{succ u2} (Multiset.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f)) (Multiset.map.{u1, u2} K L (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) f)))
 Case conversion may be inaccurate. Consider using '#align polynomial.roots_map Polynomial.roots_mapₓ'. -/
 theorem roots_map {f : K[X]} (hf : f.Splits <| RingHom.id K) : (f.map i).roots = f.roots.map i :=
   (roots_map_of_injective_of_card_eq_natDegree i.Injective <|
@@ -530,7 +530,7 @@ theorem adjoin_rootSet_eq_range [Algebra F K] [Algebra F L] {p : F[X]}
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {p : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))} {i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i p) -> (Eq.{succ u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i p) (HMul.hMul.{u2, u2, u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (instHMul.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.mul'.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (fun (_x : RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) => L -> (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Polynomial.C.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (fun (_x : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) => K -> L) (RingHom.hasCoeToFun.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) i (Polynomial.leadingCoeff.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) p))) (Multiset.prod.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (CommRing.toCommMonoid.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)))) (Multiset.map.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (fun (a : L) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (instHSub.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.sub.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.X.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (fun (_x : RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) => L -> (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Polynomial.C.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) a)) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i p))))))
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))} {i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i p) -> (Eq.{succ u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p))) (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p))) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 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(DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p))) (Polynomial.mul'.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun 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(Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))))) (Polynomial.C.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a)) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p))))))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))} {i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i p) -> (Eq.{succ u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p))) (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p))) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p))) (Polynomial.mul'.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K 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(Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : L) => Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))))) (Polynomial.C.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a)) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_prod_roots_of_splits Polynomial.eq_prod_roots_of_splitsₓ'. -/
 theorem eq_prod_roots_of_splits {p : K[X]} {i : K →+* L} (hsplit : Splits i p) :
     p.map i = C (i p.leadingCoeff) * ((p.map i).roots.map fun a => X - C a).Prod :=
@@ -544,7 +544,7 @@ theorem eq_prod_roots_of_splits {p : K[X]} {i : K →+* L} (hsplit : Splits i p)
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) p) -> (Eq.{succ u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) p (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (instHMul.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.mul'.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.leadingCoeff.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) p)) (Multiset.prod.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.commRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)))) (Multiset.map.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (fun (a : K) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (instHSub.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.X.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) a)) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) p)))))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) p) -> (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) p (HMul.hMul.{u1, u1, u1} ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (instHMul.{u1} ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.mul'.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Multiset.prod.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} K _inst_1))) (Multiset.map.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (fun (a : K) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) ((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_1)))) a) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) a)) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) p)))))
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) p) -> (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) p (HMul.hMul.{u1, u1, u1} ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (instHMul.{u1} ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.mul'.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Multiset.prod.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.commRing.{u1} K (Field.toCommRing.{u1} K _inst_1))) (Multiset.map.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (fun (a : K) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) ((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_1)))) a) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) a)) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) p)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_prod_roots_of_splits_id Polynomial.eq_prod_roots_of_splits_idₓ'. -/
 theorem eq_prod_roots_of_splits_id {p : K[X]} (hsplit : Splits (RingHom.id K) p) :
     p = C p.leadingCoeff * (p.roots.map fun a => X - C a).Prod := by
@@ -555,7 +555,7 @@ theorem eq_prod_roots_of_splits_id {p : K[X]} (hsplit : Splits (RingHom.id K) p)
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Polynomial.Monic.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) p) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) p) -> (Eq.{succ u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) p (Multiset.prod.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.commRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)))) (Multiset.map.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (fun (a : K) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (instHSub.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.X.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) a)) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) p))))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Monic.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) p) -> (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) p (Multiset.prod.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} K _inst_1))) (Multiset.map.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (fun (a : K) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) ((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_1)))) a) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) a)) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) p))))
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Monic.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) p) -> (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) p (Multiset.prod.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.commRing.{u1} K (Field.toCommRing.{u1} K _inst_1))) (Multiset.map.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (fun (a : K) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) ((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_1)))) a) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) a)) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) p))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_prod_roots_of_monic_of_splits_id Polynomial.eq_prod_roots_of_monic_of_splits_idₓ'. -/
 theorem eq_prod_roots_of_monic_of_splits_id {p : K[X]} (m : Monic p)
     (hsplit : Splits (RingHom.id K) p) : p = (p.roots.map fun a => X - C a).Prod :=
@@ -568,7 +568,7 @@ theorem eq_prod_roots_of_monic_of_splits_id {p : K[X]} (m : Monic p)
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {x : K} {h : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i h) -> (Eq.{succ u2} (Multiset.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i h)) (Singleton.singleton.{u2, u2} L (Multiset.{u2} L) (Multiset.hasSingleton.{u2} L) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (fun (_x : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) => K -> L) (RingHom.hasCoeToFun.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) i x))) -> (Eq.{succ u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) h (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (instHMul.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.mul'.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.leadingCoeff.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) h)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (instHSub.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.X.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) x))))
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {x : K} {h : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i h) -> (Eq.{succ u2} (Multiset.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i h)) (Singleton.singleton.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) x) (Multiset.{u2} L) (Multiset.instSingletonMultiset.{u2} L) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))))) i x))) -> (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) h (HMul.hMul.{u1, u1, u1} ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) h)) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (instHMul.{u1} ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) h)) (Polynomial.mul'.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) h)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) ((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_1)))) x) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) x))))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {x : K} {h : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i h) -> (Eq.{succ u2} (Multiset.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i h)) (Singleton.singleton.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) x) (Multiset.{u2} L) (Multiset.instSingletonMultiset.{u2} L) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i x))) -> (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) h (HMul.hMul.{u1, u1, u1} ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) h)) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (instHMul.{u1} ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) h)) (Polynomial.mul'.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) h)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) ((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_1)))) x) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) x))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_X_sub_C_of_splits_of_single_root Polynomial.eq_X_sub_C_of_splits_of_single_rootₓ'. -/
 theorem eq_X_sub_C_of_splits_of_single_root {x : K} {h : K[X]} (h_splits : Splits i h)
     (h_roots : (h.map i).roots = {i x}) : h = C h.leadingCoeff * (X - C x) :=
@@ -582,7 +582,7 @@ theorem eq_X_sub_C_of_splits_of_single_root {x : K} {h : K[X]} (h_splits : Split
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] (R : Type.{u2}) [_inst_4 : CommRing.{u2} R] [_inst_5 : Algebra.{u2, u1} R K (CommRing.toCommSemiring.{u2} R _inst_4) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))] {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) f) -> (Polynomial.Monic.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) f) -> (forall (a : K), (Membership.Mem.{u1, u1} K (Multiset.{u1} K) (Multiset.hasMem.{u1} K) a (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) f)) -> (Membership.Mem.{u1, u1} K (Subring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (SetLike.hasMem.{u1, u1} (Subring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) K (Subring.setLike.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) a (RingHom.range.{u2, u1} R K (CommRing.toRing.{u2} R _inst_4) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (algebraMap.{u2, u1} R K (CommRing.toCommSemiring.{u2} R _inst_4) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_5)))) -> (Membership.Mem.{u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subsemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (SetLike.hasMem.{u1, u1} (Subsemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subsemiring.setLike.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) f (Polynomial.lifts.{u2, u1} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (algebraMap.{u2, u1} R K (CommRing.toCommSemiring.{u2} R _inst_4) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_5)))
 but is expected to have type
-  forall {K : Type.{u2}} [_inst_1 : Field.{u2} K] (R : Type.{u1}) [_inst_4 : CommRing.{u1} R] [_inst_5 : Algebra.{u1, u2} R K (CommRing.toCommSemiring.{u1} R _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))] {f : Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))}, (Polynomial.Splits.{u2, u2} K K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) _inst_1 (RingHom.id.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1))))) f) -> (Polynomial.Monic.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) f) -> (forall (a : K), (Membership.mem.{u2, u2} K (Multiset.{u2} K) (Multiset.instMembershipMultiset.{u2} K) a (Polynomial.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) f)) -> (Membership.mem.{u2, u2} K (Subring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1))) (SetLike.instMembership.{u2, u2} (Subring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1))) K (Subring.instSetLikeSubring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))) a (RingHom.range.{u1, u2} R K (CommRing.toRing.{u1} R _inst_4) (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)) (algebraMap.{u1, u2} R K (CommRing.toCommSemiring.{u1} R _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_5)))) -> (Membership.mem.{u2, u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Subsemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))) f (Polynomial.lifts.{u1, u2} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (algebraMap.{u1, u2} R K (CommRing.toCommSemiring.{u1} R _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_5)))
+  forall {K : Type.{u2}} [_inst_1 : Field.{u2} K] (R : Type.{u1}) [_inst_4 : CommRing.{u1} R] [_inst_5 : Algebra.{u1, u2} R K (CommRing.toCommSemiring.{u1} R _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))] {f : Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))}, (Polynomial.Splits.{u2, u2} K K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) _inst_1 (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) f) -> (Polynomial.Monic.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) f) -> (forall (a : K), (Membership.mem.{u2, u2} K (Multiset.{u2} K) (Multiset.instMembershipMultiset.{u2} K) a (Polynomial.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) f)) -> (Membership.mem.{u2, u2} K (Subring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1))) (SetLike.instMembership.{u2, u2} (Subring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1))) K (Subring.instSetLikeSubring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))) a (RingHom.range.{u1, u2} R K (CommRing.toRing.{u1} R _inst_4) (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)) (algebraMap.{u1, u2} R K (CommRing.toCommSemiring.{u1} R _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_5)))) -> (Membership.mem.{u2, u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Subsemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))) f (Polynomial.lifts.{u1, u2} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (algebraMap.{u1, u2} R K (CommRing.toCommSemiring.{u1} R _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_5)))
 Case conversion may be inaccurate. Consider using '#align polynomial.mem_lift_of_splits_of_roots_mem_range Polynomial.mem_lift_of_splits_of_roots_mem_rangeₓ'. -/
 theorem mem_lift_of_splits_of_roots_mem_range (R : Type _) [CommRing R] [Algebra R K] {f : K[X]}
     (hs : f.Splits (RingHom.id K)) (hm : f.Monic) (hr : ∀ a ∈ f.roots, a ∈ (algebraMap R K).range) :
@@ -607,7 +607,7 @@ open UniqueFactorizationMonoid Associates
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))} {s : Multiset.{u2} L}, (Eq.{succ u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i f) (HMul.hMul.{u2, u2, u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (instHMul.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.mul'.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (fun (_x : RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) => L -> (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Polynomial.C.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (fun (_x : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) => K -> L) (RingHom.hasCoeToFun.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) i (Polynomial.leadingCoeff.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) f))) (Multiset.prod.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (CommRing.toCommMonoid.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)))) (Multiset.map.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (fun (a : L) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (instHSub.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.sub.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.X.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (fun (_x : RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) => L -> (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Polynomial.C.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) a)) s)))) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f)
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))} {s : Multiset.{u2} L}, (Eq.{succ u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f))) (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, 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(DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K 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(Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun 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L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K 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(Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f))) (Multiset.prod.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (CommRing.toCommMonoid.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)))) (Multiset.map.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (fun (a : L) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : L) => Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a) (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (instHSub.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.sub.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.X.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : L) => Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))))) (Polynomial.C.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a)) s)))) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f)
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))} {s : Multiset.{u2} L}, (Eq.{succ u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f))) (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K 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: K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))))))) (Polynomial.C.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f))) (Multiset.prod.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (CommRing.toCommMonoid.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)))) (Multiset.map.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (fun (a : L) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : L) => Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a) (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (instHSub.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.sub.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.X.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : L) => Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))))) (Polynomial.C.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a)) s)))) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f)
 Case conversion may be inaccurate. Consider using '#align polynomial.splits_of_exists_multiset Polynomial.splits_of_exists_multisetₓ'. -/
 theorem splits_of_exists_multiset {f : K[X]} {s : Multiset L}
     (hs : f.map i = C (i f.leadingCoeff) * (s.map fun a : L => X - C a).Prod) : Splits i f :=
@@ -644,7 +644,7 @@ end UFD
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, Iff (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) (Exists.{succ u2} (Multiset.{u2} L) (fun (s : Multiset.{u2} L) => Eq.{succ u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i f) (HMul.hMul.{u2, u2, u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (instHMul.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.mul'.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (fun (_x : RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) => L -> (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Polynomial.C.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (fun (_x : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) => K -> L) (RingHom.hasCoeToFun.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) i (Polynomial.leadingCoeff.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) f))) (Multiset.prod.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (CommRing.toCommMonoid.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)))) (Multiset.map.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (fun (a : L) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (instHSub.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.sub.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.X.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (fun (_x : RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) => L -> (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Polynomial.C.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) a)) s)))))
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, Iff (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) (Exists.{succ u2} (Multiset.{u2} L) (fun (s : Multiset.{u2} L) => Eq.{succ u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f))) (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f))) (instHMul.{u2} ((fun 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K 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K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) 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(Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) 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L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K (fun (_x : K) 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(NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f))) (Multiset.prod.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (CommRing.toCommMonoid.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} L _inst_2))) (Multiset.map.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (fun (a : L) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : L) => Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a) (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (instHSub.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.sub.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.X.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : L) => Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))))) (Polynomial.C.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a)) s)))))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, Iff (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) (Exists.{succ u2} (Multiset.{u2} L) (fun (s : Multiset.{u2} L) => Eq.{succ u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f))) (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) 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(Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K 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(Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))))))) (Polynomial.C.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f))) (Multiset.prod.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (CommRing.toCommMonoid.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (Field.toCommRing.{u2} L _inst_2))) (Multiset.map.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (fun (a : L) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : L) => Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a) (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (instHSub.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.sub.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.X.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : L) => Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))))) (Polynomial.C.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a)) s)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.splits_iff_exists_multiset Polynomial.splits_iff_exists_multisetₓ'. -/
 theorem splits_iff_exists_multiset {f : K[X]} :
     Splits i f ↔
@@ -667,7 +667,7 @@ theorem splits_comp_of_splits (j : L →+* F) {f : K[X]} (h : Splits i f) : Spli
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, Iff (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) p) (Eq.{1} Nat (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.orderedCancelAddCommMonoid.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.orderedCancelAddCommMonoid.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} K) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.orderedCancelAddCommMonoid.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} K) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) p)) (Polynomial.natDegree.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) p))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, Iff (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) p) (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} K) => Nat) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) p)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} K) (fun (_x : Multiset.{u1} K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} K) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} K) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} K) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} K) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) p)) (Polynomial.natDegree.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p))
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, Iff (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) p) (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} K) => Nat) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) p)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} K) (fun (_x : Multiset.{u1} K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} K) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} K) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} K) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} K) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) p)) (Polynomial.natDegree.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.splits_iff_card_roots Polynomial.splits_iff_card_rootsₓ'. -/
 /-- A polynomial splits if and only if it has as many roots as its degree. -/
 theorem splits_iff_card_roots {p : K[X]} : Splits (RingHom.id K) p ↔ p.roots.card = p.natDegree :=
@@ -699,7 +699,7 @@ theorem aeval_root_derivative_of_splits [Algebra K L] {P : K[X]} (hmo : P.Monic)
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {P : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Polynomial.Monic.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) P) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) P) -> (Eq.{succ u1} K (Polynomial.coeff.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) P (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (AddGroupWithOne.toAddGroup.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) (Polynomial.natDegree.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) P)) (Multiset.prod.{u1} K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) P))))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {P : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Monic.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) P) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) P) -> (Eq.{succ u1} K (Polynomial.coeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) P (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Polynomial.natDegree.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) P)) (Multiset.prod.{u1} K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) P))))
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {P : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Monic.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) P) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) P) -> (Eq.{succ u1} K (Polynomial.coeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) P (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Polynomial.natDegree.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) P)) (Multiset.prod.{u1} K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) P))))
 Case conversion may be inaccurate. Consider using '#align polynomial.prod_roots_eq_coeff_zero_of_monic_of_split Polynomial.prod_roots_eq_coeff_zero_of_monic_of_splitₓ'. -/
 /-- If `P` is a monic polynomial that splits, then `coeff P 0` equals the product of the roots. -/
 theorem prod_roots_eq_coeff_zero_of_monic_of_split {P : K[X]} (hmo : P.Monic)
@@ -721,7 +721,7 @@ theorem prod_roots_eq_coeff_zero_of_monic_of_split {P : K[X]} (hmo : P.Monic)
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {P : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Polynomial.Monic.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) P) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) P) -> (Eq.{succ u1} K (Polynomial.nextCoeff.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) P) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (AddGroupWithOne.toAddGroup.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Multiset.sum.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) P))))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {P : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Monic.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) P) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) P) -> (Eq.{succ u1} K (Polynomial.nextCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) P) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Multiset.sum.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) P))))
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {P : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Monic.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) P) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) P) -> (Eq.{succ u1} K (Polynomial.nextCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) P) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Multiset.sum.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) P))))
 Case conversion may be inaccurate. Consider using '#align polynomial.sum_roots_eq_next_coeff_of_monic_of_split Polynomial.sum_roots_eq_nextCoeff_of_monic_of_splitₓ'. -/
 /-- If `P` is a monic polynomial that splits, then `P.next_coeff` equals the sum of the roots. -/
 theorem sum_roots_eq_nextCoeff_of_monic_of_split {P : K[X]} (hmo : P.Monic)

mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c

@@ -596,7 +596,7 @@ theorem mem_lift_of_splits_of_roots_mem_range (R : Type _) [CommRing R] [Algebra
 
 section UFD
 
-attribute [local instance] PrincipalIdealRing.to_uniqueFactorizationMonoid
+attribute [local instance 10] PrincipalIdealRing.to_uniqueFactorizationMonoid
 
 -- mathport name: «expr ~ᵤ »
 local infixl:50 " ~ᵤ " => Associated

mathlib commit https://github.com/leanprover-community/mathlib/commit/3cacc945118c8c637d89950af01da78307f59325

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 
 ! This file was ported from Lean 3 source module data.polynomial.splits
-! leanprover-community/mathlib commit f694c7dead66f5d4c80f446c796a5aad14707f0e
+! leanprover-community/mathlib commit 31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Data.Polynomial.Lifts
 /-!
 # Split polynomials
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 A polynomial `f : K[X]` splits over a field extension `L` of `K` if it is zero or all of its
 irreducible factors over `L` have degree `1`.
 

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

@@ -53,17 +53,27 @@ variable [CommRing K] [Field L] [Field F]
 
 variable (i : K →+* L)
 
+#print Polynomial.Splits /-
 /-- A polynomial `splits` iff it is zero or all of its irreducible factors have `degree` 1. -/
 def Splits (f : K[X]) : Prop :=
   f.map i = 0 ∨ ∀ {g : L[X]}, Irreducible g → g ∣ f.map i → degree g = 1
 #align polynomial.splits Polynomial.Splits
+-/
 
+#print Polynomial.splits_zero /-
 @[simp]
 theorem splits_zero : Splits i (0 : K[X]) :=
   Or.inl (Polynomial.map_zero i)
 #align polynomial.splits_zero Polynomial.splits_zero
+-/
 
-theorem splits_of_map_eq_c {f : K[X]} {a : L} (h : f.map i = C a) : Splits i f :=
+/- warning: polynomial.splits_of_map_eq_C -> Polynomial.splits_of_map_eq_C is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))} {a : L}, (Eq.{succ u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i f) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (fun (_x : RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) => L -> (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Polynomial.C.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) a)) -> (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i f)
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))} {a : L}, (Eq.{succ u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : L) => Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} L (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))))) (Polynomial.C.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a)) -> (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i f)
+Case conversion may be inaccurate. Consider using '#align polynomial.splits_of_map_eq_C Polynomial.splits_of_map_eq_Cₓ'. -/
+theorem splits_of_map_eq_C {f : K[X]} {a : L} (h : f.map i = C a) : Splits i f :=
   if ha : a = 0 then Or.inl (h.trans (ha.symm ▸ C_0))
   else
     Or.inr fun g hg ⟨p, hp⟩ =>
@@ -74,13 +84,20 @@ theorem splits_of_map_eq_c {f : K[X]} {a : L} (h : f.map i = C a) : Splits i f :
             rw [h, degree_C ha, degree_mul, @eq_comm (WithBot ℕ) 0, Nat.WithBot.add_eq_zero_iff] at
               this
             exact this.1
-#align polynomial.splits_of_map_eq_C Polynomial.splits_of_map_eq_c
-
+#align polynomial.splits_of_map_eq_C Polynomial.splits_of_map_eq_C
+
+/- warning: polynomial.splits_C -> Polynomial.splits_C is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (a : K), Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) a)
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (a : K), Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)))))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) a)
+Case conversion may be inaccurate. Consider using '#align polynomial.splits_C Polynomial.splits_Cₓ'. -/
 @[simp]
-theorem splits_c (a : K) : Splits i (C a) :=
-  splits_of_map_eq_c i (map_C i)
-#align polynomial.splits_C Polynomial.splits_c
+theorem splits_C (a : K) : Splits i (C a) :=
+  splits_of_map_eq_C i (map_C i)
+#align polynomial.splits_C Polynomial.splits_C
 
+#print Polynomial.splits_of_map_degree_eq_one /-
 theorem splits_of_map_degree_eq_one {f : K[X]} (hf : degree (f.map i) = 1) : Splits i f :=
   Or.inr fun g hg ⟨p, hp⟩ => by
     have := congr_arg degree hp <;>
@@ -89,27 +106,37 @@ theorem splits_of_map_degree_eq_one {f : K[X]} (hf : degree (f.map i) = 1) : Spl
         clear _fun_match <;>
       tauto
 #align polynomial.splits_of_map_degree_eq_one Polynomial.splits_of_map_degree_eq_one
+-/
 
+#print Polynomial.splits_of_degree_le_one /-
 theorem splits_of_degree_le_one {f : K[X]} (hf : degree f ≤ 1) : Splits i f :=
-  if hif : degree (f.map i) ≤ 0 then splits_of_map_eq_c i (degree_le_zero_iff.mp hif)
+  if hif : degree (f.map i) ≤ 0 then splits_of_map_eq_C i (degree_le_zero_iff.mp hif)
   else by
     push_neg  at hif
     rw [← Order.succ_le_iff, ← WithBot.coe_zero, WithBot.succ_coe, Nat.succ_eq_succ] at hif
     exact splits_of_map_degree_eq_one i (le_antisymm ((degree_map_le i _).trans hf) hif)
 #align polynomial.splits_of_degree_le_one Polynomial.splits_of_degree_le_one
+-/
 
+#print Polynomial.splits_of_degree_eq_one /-
 theorem splits_of_degree_eq_one {f : K[X]} (hf : degree f = 1) : Splits i f :=
   splits_of_degree_le_one i hf.le
 #align polynomial.splits_of_degree_eq_one Polynomial.splits_of_degree_eq_one
+-/
 
+#print Polynomial.splits_of_natDegree_le_one /-
 theorem splits_of_natDegree_le_one {f : K[X]} (hf : natDegree f ≤ 1) : Splits i f :=
   splits_of_degree_le_one i (degree_le_of_natDegree_le hf)
 #align polynomial.splits_of_nat_degree_le_one Polynomial.splits_of_natDegree_le_one
+-/
 
+#print Polynomial.splits_of_natDegree_eq_one /-
 theorem splits_of_natDegree_eq_one {f : K[X]} (hf : natDegree f = 1) : Splits i f :=
   splits_of_natDegree_le_one i (le_of_eq hf)
 #align polynomial.splits_of_nat_degree_eq_one Polynomial.splits_of_natDegree_eq_one
+-/
 
+#print Polynomial.splits_mul /-
 theorem splits_mul {f g : K[X]} (hf : Splits i f) (hg : Splits i g) : Splits i (f * g) :=
   if h : (f * g).map i = 0 then Or.inl h
   else
@@ -119,7 +146,9 @@ theorem splits_mul {f g : K[X]} (hf : Splits i f) (hg : Splits i g) : Splits i (
         (hf.resolve_left (fun hf => by simpa [hf] using h) hp)
         (hg.resolve_left (fun hg => by simpa [hg] using h) hp)
 #align polynomial.splits_mul Polynomial.splits_mul
+-/
 
+#print Polynomial.splits_of_splits_mul' /-
 theorem splits_of_splits_mul' {f g : K[X]} (hfg : (f * g).map i ≠ 0) (h : Splits i (f * g)) :
     Splits i f ∧ Splits i g :=
   ⟨Or.inr fun g hgi hg =>
@@ -127,27 +156,47 @@ theorem splits_of_splits_mul' {f g : K[X]} (hfg : (f * g).map i ≠ 0) (h : Spli
     Or.inr fun g hgi hg =>
       Or.resolve_left h hfg hgi (by rw [Polynomial.map_mul] <;> exact hg.trans (dvd_mul_left _ _))⟩
 #align polynomial.splits_of_splits_mul' Polynomial.splits_of_splits_mul'
+-/
 
+#print Polynomial.splits_map_iff /-
 theorem splits_map_iff (j : L →+* F) {f : K[X]} : Splits j (f.map i) ↔ Splits (j.comp i) f := by
   simp [splits, Polynomial.map_map]
 #align polynomial.splits_map_iff Polynomial.splits_map_iff
+-/
 
+#print Polynomial.splits_one /-
 theorem splits_one : Splits i 1 :=
-  splits_c i 1
+  splits_C i 1
 #align polynomial.splits_one Polynomial.splits_one
+-/
 
+/- warning: polynomial.splits_of_is_unit -> Polynomial.splits_of_isUnit is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) [_inst_4 : IsDomain.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))] {u : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))}, (IsUnit.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.ring.{u1} K (CommRing.toRing.{u1} K _inst_1))) u) -> (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i u)
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) [_inst_4 : IsDomain.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))] {u : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))}, (IsUnit.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) u) -> (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i u)
+Case conversion may be inaccurate. Consider using '#align polynomial.splits_of_is_unit Polynomial.splits_of_isUnitₓ'. -/
 theorem splits_of_isUnit [IsDomain K] {u : K[X]} (hu : IsUnit u) : u.Splits i :=
-  (isUnit_iff.mp hu).choose_spec.2 ▸ splits_c _ _
+  (isUnit_iff.mp hu).choose_spec.2 ▸ splits_C _ _
 #align polynomial.splits_of_is_unit Polynomial.splits_of_isUnit
 
-theorem splits_x_sub_c {x : K} : (X - C x).Splits i :=
+/- warning: polynomial.splits_X_sub_C -> Polynomial.splits_X_sub_C is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {x : K}, Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (instHSub.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.sub.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.X.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) x))
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {x : K}, Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) x) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (instHSub.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.sub.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.X.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)))))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) x))
+Case conversion may be inaccurate. Consider using '#align polynomial.splits_X_sub_C Polynomial.splits_X_sub_Cₓ'. -/
+theorem splits_X_sub_C {x : K} : (X - C x).Splits i :=
   splits_of_degree_le_one _ <| degree_X_sub_C_le _
-#align polynomial.splits_X_sub_C Polynomial.splits_x_sub_c
+#align polynomial.splits_X_sub_C Polynomial.splits_X_sub_C
 
-theorem splits_x : X.Splits i :=
+#print Polynomial.splits_X /-
+theorem splits_X : X.Splits i :=
   splits_of_degree_le_one _ degree_X_le
-#align polynomial.splits_X Polynomial.splits_x
+#align polynomial.splits_X Polynomial.splits_X
+-/
 
+#print Polynomial.splits_prod /-
 theorem splits_prod {ι : Type u} {s : ι → K[X]} {t : Finset ι} :
     (∀ j ∈ t, (s j).Splits i) → (∏ x in t, s x).Splits i :=
   by
@@ -155,21 +204,42 @@ theorem splits_prod {ι : Type u} {s : ι → K[X]} {t : Finset ι} :
   rw [Finset.forall_mem_insert] at ht; rw [Finset.prod_insert hat]
   exact splits_mul i ht.1 (ih ht.2)
 #align polynomial.splits_prod Polynomial.splits_prod
+-/
 
+/- warning: polynomial.splits_pow -> Polynomial.splits_pow is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))}, (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i f) -> (forall (n : Nat), Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) Nat (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.ring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) f n))
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))}, (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i f) -> (forall (n : Nat), Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) Nat (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))))) f n))
+Case conversion may be inaccurate. Consider using '#align polynomial.splits_pow Polynomial.splits_powₓ'. -/
 theorem splits_pow {f : K[X]} (hf : f.Splits i) (n : ℕ) : (f ^ n).Splits i :=
   by
   rw [← Finset.card_range n, ← Finset.prod_const]
   exact splits_prod i fun j hj => hf
 #align polynomial.splits_pow Polynomial.splits_pow
 
-theorem splits_x_pow (n : ℕ) : (X ^ n).Splits i :=
-  splits_pow i (splits_x i) n
-#align polynomial.splits_X_pow Polynomial.splits_x_pow
-
+/- warning: polynomial.splits_X_pow -> Polynomial.splits_X_pow is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (n : Nat), Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) Nat (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.ring.{u1} K (CommRing.toRing.{u1} K _inst_1))))) (Polynomial.X.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) n)
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (n : Nat), Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) Nat (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))))))) (Polynomial.X.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) n)
+Case conversion may be inaccurate. Consider using '#align polynomial.splits_X_pow Polynomial.splits_X_powₓ'. -/
+theorem splits_X_pow (n : ℕ) : (X ^ n).Splits i :=
+  splits_pow i (splits_X i) n
+#align polynomial.splits_X_pow Polynomial.splits_X_pow
+
+#print Polynomial.splits_id_iff_splits /-
 theorem splits_id_iff_splits {f : K[X]} : (f.map i).Splits (RingHom.id L) ↔ f.Splits i := by
   rw [splits_map_iff, RingHom.id_comp]
 #align polynomial.splits_id_iff_splits Polynomial.splits_id_iff_splits
+-/
 
+/- warning: polynomial.exists_root_of_splits' -> Polynomial.exists_root_of_splits' is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))}, (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i f) -> (Ne.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i f)) (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))))) -> (Exists.{succ u2} L (fun (x : L) => Eq.{succ u2} L (Polynomial.eval₂.{u1, u2} K L (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i x f) (OfNat.ofNat.{u2} L 0 (OfNat.mk.{u2} L 0 (Zero.zero.{u2} L (MulZeroClass.toHasZero.{u2} L (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))))))
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : CommRing.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))}, (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i f) -> (Ne.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f)) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) -> (Exists.{succ u2} L (fun (x : L) => Eq.{succ u2} L (Polynomial.eval₂.{u1, u2} K L (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i x f) (OfNat.ofNat.{u2} L 0 (Zero.toOfNat0.{u2} L (CommMonoidWithZero.toZero.{u2} L (CommGroupWithZero.toCommMonoidWithZero.{u2} L (Semifield.toCommGroupWithZero.{u2} L (Field.toSemifield.{u2} L _inst_2))))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.exists_root_of_splits' Polynomial.exists_root_of_splits'ₓ'. -/
 theorem exists_root_of_splits' {f : K[X]} (hs : Splits i f) (hf0 : degree (f.map i) ≠ 0) :
     ∃ x, eval₂ i x f = 0 :=
   if hf0' : f.map i = 0 then by simp [eval₂_eq_eval_map, hf0']
@@ -182,6 +252,7 @@ theorem exists_root_of_splits' {f : K[X]} (hs : Splits i f) (hf0 : degree (f.map
     ⟨x, by rw [← eval_map, hi, eval_mul, show _ = _ from hx, MulZeroClass.zero_mul]⟩
 #align polynomial.exists_root_of_splits' Polynomial.exists_root_of_splits'
 
+#print Polynomial.roots_ne_zero_of_splits' /-
 theorem roots_ne_zero_of_splits' {f : K[X]} (hs : Splits i f) (hf0 : natDegree (f.map i) ≠ 0) :
     (f.map i).roots ≠ 0 :=
   let ⟨x, hx⟩ := exists_root_of_splits' i hs fun h => hf0 <| natDegree_eq_of_degree_eq_some h
@@ -190,18 +261,33 @@ theorem roots_ne_zero_of_splits' {f : K[X]} (hs : Splits i f) (hf0 : natDegree (
   cases h.subst ((mem_roots _).2 hx)
   exact ne_zero_of_nat_degree_gt (Nat.pos_of_ne_zero hf0)
 #align polynomial.roots_ne_zero_of_splits' Polynomial.roots_ne_zero_of_splits'
+-/
 
+#print Polynomial.rootOfSplits' /-
 /-- Pick a root of a polynomial that splits. See `root_of_splits` for polynomials over a field
 which has simpler assumptions. -/
 def rootOfSplits' {f : K[X]} (hf : f.Splits i) (hfd : (f.map i).degree ≠ 0) : L :=
   Classical.choose <| exists_root_of_splits' i hf hfd
 #align polynomial.root_of_splits' Polynomial.rootOfSplits'
+-/
 
+/- warning: polynomial.map_root_of_splits' -> Polynomial.map_rootOfSplits' 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_root_of_splits' Polynomial.map_rootOfSplits'ₓ'. -/
 theorem map_rootOfSplits' {f : K[X]} (hf : f.Splits i) (hfd) :
     f.eval₂ i (rootOfSplits' i hf hfd) = 0 :=
   Classical.choose_spec <| exists_root_of_splits' i hf hfd
 #align polynomial.map_root_of_splits' Polynomial.map_rootOfSplits'
 
+/- warning: polynomial.nat_degree_eq_card_roots' -> Polynomial.natDegree_eq_card_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.nat_degree_eq_card_roots' Polynomial.natDegree_eq_card_roots'ₓ'. -/
 theorem natDegree_eq_card_roots' {p : K[X]} {i : K →+* L} (hsplit : Splits i p) :
     (p.map i).natDegree = (p.map i).roots.card :=
   by
@@ -221,6 +307,12 @@ theorem natDegree_eq_card_roots' {p : K[X]} {i : K →+* L} (hsplit : Splits i p
     exact mul_ne_zero monic_prod_multiset_X_sub_C.ne_zero hq
 #align polynomial.nat_degree_eq_card_roots' Polynomial.natDegree_eq_card_roots'
 
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(DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.zero.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) -> (Polynomial.Splits.{u1, u2} K L _inst_1 _inst_2 i p) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) (fun (_x : Multiset.{u2} L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} L) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} L) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p)))))
+Case conversion may be inaccurate. Consider using '#align polynomial.degree_eq_card_roots' Polynomial.degree_eq_card_roots'ₓ'. -/
 theorem degree_eq_card_roots' {p : K[X]} {i : K →+* L} (p_ne_zero : p.map i ≠ 0)
     (hsplit : Splits i p) : (p.map i).degree = (p.map i).roots.card := by
   rw [degree_eq_nat_degree p_ne_zero, nat_degree_eq_card_roots' hsplit]
@@ -232,44 +324,75 @@ variable [Field K] [Field L] [Field F]
 
 variable (i : K →+* L)
 
+/- warning: polynomial.splits_iff -> Polynomial.splits_iff is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))), Iff (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) (Or (Eq.{succ u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) f (OfNat.ofNat.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.zero.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (forall {g : Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))}, (Irreducible.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Ring.toMonoid.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.ring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) g) -> (Dvd.Dvd.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (semigroupDvd.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (SemigroupWithZero.toSemigroup.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (NonUnitalSemiring.toSemigroupWithZero.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (NonUnitalRing.toNonUnitalSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (NonUnitalCommRing.toNonUnitalRing.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (CommRing.toNonUnitalCommRing.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2))))))))) g (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i f)) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) g) (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 {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))), Iff (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) (Or (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) f (OfNat.ofNat.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.zero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (forall {g : Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))}, (Irreducible.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (MonoidWithZero.toMonoid.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toMonoidWithZero.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) g) -> (Dvd.dvd.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (semigroupDvd.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (SemigroupWithZero.toSemigroup.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalSemiring.toSemigroupWithZero.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalRing.toNonUnitalSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalCommRing.toNonUnitalRing.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (CommRing.toNonUnitalCommRing.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} L _inst_2)))))))) g (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f)) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) g) (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.splits_iff Polynomial.splits_iffₓ'. -/
 /-- This lemma is for polynomials over a field. -/
 theorem splits_iff (f : K[X]) :
     Splits i f ↔ f = 0 ∨ ∀ {g : L[X]}, Irreducible g → g ∣ f.map i → degree g = 1 := by
   rw [splits, map_eq_zero]
 #align polynomial.splits_iff Polynomial.splits_iff
 
+/- warning: polynomial.splits.def -> Polynomial.Splits.def is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))} {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) -> (Or (Eq.{succ u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) f (OfNat.ofNat.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.zero.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (forall {g : Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))}, (Irreducible.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Ring.toMonoid.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.ring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) g) -> (Dvd.Dvd.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (semigroupDvd.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (SemigroupWithZero.toSemigroup.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (NonUnitalSemiring.toSemigroupWithZero.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (NonUnitalRing.toNonUnitalSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (NonUnitalCommRing.toNonUnitalRing.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (CommRing.toNonUnitalCommRing.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2))))))))) g (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i f)) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) g) (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 {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))} {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) -> (Or (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) f (OfNat.ofNat.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.zero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (forall {g : Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))}, (Irreducible.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (MonoidWithZero.toMonoid.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Semiring.toMonoidWithZero.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) g) -> (Dvd.dvd.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (semigroupDvd.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (SemigroupWithZero.toSemigroup.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalSemiring.toSemigroupWithZero.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalRing.toNonUnitalSemiring.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (NonUnitalCommRing.toNonUnitalRing.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (CommRing.toNonUnitalCommRing.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (EuclideanDomain.toCommRing.{u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u2} L _inst_2)))))))) g (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f)) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) g) (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.splits.def Polynomial.Splits.defₓ'. -/
 /-- This lemma is for polynomials over a field. -/
 theorem Splits.def {i : K →+* L} {f : K[X]} (h : Splits i f) :
     f = 0 ∨ ∀ {g : L[X]}, Irreducible g → g ∣ f.map i → degree g = 1 :=
   (splits_iff i f).mp h
 #align polynomial.splits.def Polynomial.Splits.def
 
+#print Polynomial.splits_of_splits_mul /-
 theorem splits_of_splits_mul {f g : K[X]} (hfg : f * g ≠ 0) (h : Splits i (f * g)) :
     Splits i f ∧ Splits i g :=
   splits_of_splits_mul' i (map_ne_zero hfg) h
 #align polynomial.splits_of_splits_mul Polynomial.splits_of_splits_mul
+-/
 
+#print Polynomial.splits_of_splits_of_dvd /-
 theorem splits_of_splits_of_dvd {f g : K[X]} (hf0 : f ≠ 0) (hf : Splits i f) (hgf : g ∣ f) :
     Splits i g := by
   obtain ⟨f, rfl⟩ := hgf
   exact (splits_of_splits_mul i hf0 hf).1
 #align polynomial.splits_of_splits_of_dvd Polynomial.splits_of_splits_of_dvd
+-/
 
+/- warning: polynomial.splits_of_splits_gcd_left -> Polynomial.splits_of_splits_gcd_left is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))} {g : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) f (OfNat.ofNat.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.zero.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i (EuclideanDomain.gcd.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) (Polynomial.euclideanDomain.{u1} K _inst_1) (fun (a : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) (b : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) a b)) f g))
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))} {g : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) f (OfNat.ofNat.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.zero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i (EuclideanDomain.gcd.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} K _inst_1) (fun (a : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) (b : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) a b)) f g))
+Case conversion may be inaccurate. Consider using '#align polynomial.splits_of_splits_gcd_left Polynomial.splits_of_splits_gcd_leftₓ'. -/
 theorem splits_of_splits_gcd_left {f g : K[X]} (hf0 : f ≠ 0) (hf : Splits i f) :
     Splits i (EuclideanDomain.gcd f g) :=
   Polynomial.splits_of_splits_of_dvd i hf0 hf (EuclideanDomain.gcd_dvd_left f g)
 #align polynomial.splits_of_splits_gcd_left Polynomial.splits_of_splits_gcd_left
 
+/- warning: polynomial.splits_of_splits_gcd_right -> Polynomial.splits_of_splits_gcd_right is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))} {g : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) g (OfNat.ofNat.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.zero.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i g) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i (EuclideanDomain.gcd.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) (Polynomial.euclideanDomain.{u1} K _inst_1) (fun (a : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) (b : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) a b)) f g))
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))} {g : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Ne.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) g (OfNat.ofNat.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.zero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i g) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i (EuclideanDomain.gcd.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} K _inst_1) (fun (a : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) (b : Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))) a b)) f g))
+Case conversion may be inaccurate. Consider using '#align polynomial.splits_of_splits_gcd_right Polynomial.splits_of_splits_gcd_rightₓ'. -/
 theorem splits_of_splits_gcd_right {f g : K[X]} (hg0 : g ≠ 0) (hg : Splits i g) :
     Splits i (EuclideanDomain.gcd f g) :=
   Polynomial.splits_of_splits_of_dvd i hg0 hg (EuclideanDomain.gcd_dvd_right f g)
 #align polynomial.splits_of_splits_gcd_right Polynomial.splits_of_splits_gcd_right
 
+#print Polynomial.splits_mul_iff /-
 theorem splits_mul_iff {f g : K[X]} (hf : f ≠ 0) (hg : g ≠ 0) :
     (f * g).Splits i ↔ f.Splits i ∧ g.Splits i :=
   ⟨splits_of_splits_mul i (mul_ne_zero hf hg), fun ⟨hfs, hgs⟩ => splits_mul i hfs hgs⟩
 #align polynomial.splits_mul_iff Polynomial.splits_mul_iff
+-/
 
+#print Polynomial.splits_prod_iff /-
 theorem splits_prod_iff {ι : Type u} {s : ι → K[X]} {t : Finset ι} :
     (∀ j ∈ t, s j ≠ 0) → ((∏ x in t, s x).Splits i ↔ ∀ j ∈ t, (s j).Splits i) :=
   by
@@ -279,7 +402,14 @@ theorem splits_prod_iff {ι : Type u} {s : ι → K[X]} {t : Finset ι} :
   rw [Finset.forall_mem_insert] at ht⊢
   rw [Finset.prod_insert hat, splits_mul_iff i ht.1 (Finset.prod_ne_zero_iff.2 ht.2), ih ht.2]
 #align polynomial.splits_prod_iff Polynomial.splits_prod_iff
+-/
 
+/- warning: polynomial.degree_eq_one_of_irreducible_of_splits -> Polynomial.degree_eq_one_of_irreducible_of_splits is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.ring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) p) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) p) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _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 {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) p) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) p) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _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_splits Polynomial.degree_eq_one_of_irreducible_of_splitsₓ'. -/
 theorem degree_eq_one_of_irreducible_of_splits {p : K[X]} (hp : Irreducible p)
     (hp_splits : Splits (RingHom.id K) p) : p.degree = 1 :=
   by
@@ -290,43 +420,79 @@ theorem degree_eq_one_of_irreducible_of_splits {p : K[X]} (hp : Irreducible p)
     simp
 #align polynomial.degree_eq_one_of_irreducible_of_splits Polynomial.degree_eq_one_of_irreducible_of_splits
 
+/- warning: polynomial.exists_root_of_splits -> Polynomial.exists_root_of_splits is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) -> (Ne.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) f) (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))))) -> (Exists.{succ u2} L (fun (x : L) => Eq.{succ u2} L (Polynomial.eval₂.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i x f) (OfNat.ofNat.{u2} L 0 (OfNat.mk.{u2} L 0 (Zero.zero.{u2} L (MulZeroClass.toHasZero.{u2} L (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))))))
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) -> (Ne.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))) -> (Exists.{succ u2} L (fun (x : L) => Eq.{succ u2} L (Polynomial.eval₂.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i x f) (OfNat.ofNat.{u2} L 0 (Zero.toOfNat0.{u2} L (CommMonoidWithZero.toZero.{u2} L (CommGroupWithZero.toCommMonoidWithZero.{u2} L (Semifield.toCommGroupWithZero.{u2} L (Field.toSemifield.{u2} L _inst_2))))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.exists_root_of_splits Polynomial.exists_root_of_splitsₓ'. -/
 theorem exists_root_of_splits {f : K[X]} (hs : Splits i f) (hf0 : degree f ≠ 0) :
     ∃ x, eval₂ i x f = 0 :=
   exists_root_of_splits' i hs ((f.degree_map i).symm ▸ hf0)
 #align polynomial.exists_root_of_splits Polynomial.exists_root_of_splits
 
+#print Polynomial.roots_ne_zero_of_splits /-
 theorem roots_ne_zero_of_splits {f : K[X]} (hs : Splits i f) (hf0 : natDegree f ≠ 0) :
     (f.map i).roots ≠ 0 :=
   roots_ne_zero_of_splits' i hs (ne_of_eq_of_ne (natDegree_map i) hf0)
 #align polynomial.roots_ne_zero_of_splits Polynomial.roots_ne_zero_of_splits
+-/
 
+#print Polynomial.rootOfSplits /-
 /-- Pick a root of a polynomial that splits. This version is for polynomials over a field and has
 simpler assumptions. -/
 def rootOfSplits {f : K[X]} (hf : f.Splits i) (hfd : f.degree ≠ 0) : L :=
   rootOfSplits' i hf ((f.degree_map i).symm ▸ hfd)
 #align polynomial.root_of_splits Polynomial.rootOfSplits
+-/
 
+#print Polynomial.rootOfSplits'_eq_rootOfSplits /-
 /-- `root_of_splits'` is definitionally equal to `root_of_splits`. -/
 theorem rootOfSplits'_eq_rootOfSplits {f : K[X]} (hf : f.Splits i) (hfd) :
     rootOfSplits' i hf hfd = rootOfSplits i hf (f.degree_map i ▸ hfd) :=
   rfl
 #align polynomial.root_of_splits'_eq_root_of_splits Polynomial.rootOfSplits'_eq_rootOfSplits
+-/
 
+/- warning: polynomial.map_root_of_splits -> Polynomial.map_rootOfSplits is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))} (hf : Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f) (hfd : Ne.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))), Eq.{succ u2} L (Polynomial.eval₂.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i (Polynomial.rootOfSplits.{u1, u2} K L _inst_1 _inst_2 i f hf hfd) f) (OfNat.ofNat.{u2} L 0 (Zero.toOfNat0.{u2} L (CommMonoidWithZero.toZero.{u2} L (CommGroupWithZero.toCommMonoidWithZero.{u2} L (Semifield.toCommGroupWithZero.{u2} L (Field.toSemifield.{u2} L _inst_2))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.map_root_of_splits Polynomial.map_rootOfSplitsₓ'. -/
 theorem map_rootOfSplits {f : K[X]} (hf : f.Splits i) (hfd) :
     f.eval₂ i (rootOfSplits i hf hfd) = 0 :=
   map_rootOfSplits' i hf (ne_of_eq_of_ne (degree_map f i) hfd)
 #align polynomial.map_root_of_splits Polynomial.map_rootOfSplits
 
+/- warning: polynomial.nat_degree_eq_card_roots -> Polynomial.natDegree_eq_card_roots is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {p : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))} {i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i p) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) p) (coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.orderedCancelAddCommMonoid.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.orderedCancelAddCommMonoid.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u2} L) -> Nat) (AddMonoidHom.hasCoeToFun.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.orderedCancelAddCommMonoid.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i p))))
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))} {i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i p) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p) (FunLike.coe.{succ u2, succ u2, 1} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) (fun (_x : Multiset.{u2} L) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u2} L) => Nat) _x) (AddHomClass.toFunLike.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) Nat (AddZeroClass.toAdd.{u2} (Multiset.{u2} L) (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u2, u2, 0} (AddMonoidHom.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p))))
+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_eq_card_roots Polynomial.natDegree_eq_card_rootsₓ'. -/
 theorem natDegree_eq_card_roots {p : K[X]} {i : K →+* L} (hsplit : Splits i p) :
     p.natDegree = (p.map i).roots.card :=
   (natDegree_map i).symm.trans <| natDegree_eq_card_roots' hsplit
 #align polynomial.nat_degree_eq_card_roots Polynomial.natDegree_eq_card_roots
 
+/- warning: polynomial.degree_eq_card_roots -> Polynomial.degree_eq_card_roots is a dubious translation:
+lean 3 declaration is
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(AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u2, 0} (Multiset.{u2} L) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} L) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} L) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} L) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} L) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} L) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u2} L)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p)))))
+Case conversion may be inaccurate. Consider using '#align polynomial.degree_eq_card_roots Polynomial.degree_eq_card_rootsₓ'. -/
 theorem degree_eq_card_roots {p : K[X]} {i : K →+* L} (p_ne_zero : p ≠ 0) (hsplit : Splits i p) :
     p.degree = (p.map i).roots.card := by
   rw [degree_eq_nat_degree p_ne_zero, nat_degree_eq_card_roots hsplit]
 #align polynomial.degree_eq_card_roots Polynomial.degree_eq_card_roots
 
+/- warning: polynomial.roots_map -> Polynomial.roots_map is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) f) -> (Eq.{succ u2} (Multiset.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i f)) (Multiset.map.{u1, u2} K L (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (fun (_x : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) => K -> L) (RingHom.hasCoeToFun.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) i) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) f)))
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) f) -> (Eq.{succ u2} (Multiset.{u2} L) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f)) (Multiset.map.{u1, u2} K L (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))))) i) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) f)))
+Case conversion may be inaccurate. Consider using '#align polynomial.roots_map Polynomial.roots_mapₓ'. -/
 theorem roots_map {f : K[X]} (hf : f.Splits <| RingHom.id K) : (f.map i).roots = f.roots.map i :=
   (roots_map_of_injective_of_card_eq_natDegree i.Injective <|
       by
@@ -334,13 +500,21 @@ theorem roots_map {f : K[X]} (hf : f.Splits <| RingHom.id K) : (f.map i).roots =
       rw [map_id]).symm
 #align polynomial.roots_map Polynomial.roots_map
 
+#print Polynomial.image_rootSet /-
 theorem image_rootSet [Algebra F K] [Algebra F L] {p : F[X]} (h : p.Splits (algebraMap F K))
     (f : K →ₐ[F] L) : f '' p.rootSet K = p.rootSet L := by
   classical rw [root_set, ← Finset.coe_image, ← Multiset.toFinset_map, ← f.coe_to_ring_hom, ←
       roots_map (↑f) ((splits_id_iff_splits (algebraMap F K)).mpr h), map_map, f.comp_algebra_map, ←
       root_set]
 #align polynomial.image_root_set Polynomial.image_rootSet
+-/
 
+/- warning: polynomial.adjoin_root_set_eq_range -> Polynomial.adjoin_rootSet_eq_range is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} {K : Type.{u2}} {L : Type.{u3}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u3} L] [_inst_3 : Field.{u1} F] [_inst_4 : Algebra.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))] [_inst_5 : Algebra.{u1, u3} F L (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_2)))] {p : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_3)))}, (Polynomial.Splits.{u1, u2} F K (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_3)) _inst_1 (algebraMap.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1))) _inst_4) p) -> (forall (f : AlgHom.{u1, u2, u3} F K L (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1))) (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_2))) _inst_4 _inst_5), Iff (Eq.{succ u3} (Subalgebra.{u1, u3} F L (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_2))) _inst_5) (Algebra.adjoin.{u1, u3} F L (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_2))) _inst_5 (Polynomial.rootSet.{u1, u3} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_3)) p L (EuclideanDomain.toCommRing.{u3} L (Field.toEuclideanDomain.{u3} L _inst_2)) (Field.isDomain.{u3} L _inst_2) _inst_5)) (AlgHom.range.{u1, u2, u3} F K L (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1))) _inst_4 (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_2))) _inst_5 f)) (Eq.{succ u2} (Subalgebra.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1))) _inst_4) (Algebra.adjoin.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1))) _inst_4 (Polynomial.rootSet.{u1, u2} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_3)) p K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) (Field.isDomain.{u2} K _inst_1) _inst_4)) (Top.top.{u2} (Subalgebra.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1))) _inst_4) (CompleteLattice.toHasTop.{u2} (Subalgebra.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1))) _inst_4) (Algebra.Subalgebra.completeLattice.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1))) _inst_4)))))
+but is expected to have type
+  forall {F : Type.{u1}} {K : Type.{u2}} {L : Type.{u3}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u3} L] [_inst_3 : Field.{u1} F] [_inst_4 : Algebra.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))] [_inst_5 : Algebra.{u1, u3} F L (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_2)))] {p : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)))}, (Polynomial.Splits.{u1, u2} F K (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_3)) _inst_1 (algebraMap.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_4) p) -> (forall (f : AlgHom.{u1, u2, u3} F K L (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_2))) _inst_4 _inst_5), Iff (Eq.{succ u3} (Subalgebra.{u1, u3} F L (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_2))) _inst_5) (Algebra.adjoin.{u1, u3} F L (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_2))) _inst_5 (Polynomial.rootSet.{u1, u3} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_3)) p L (EuclideanDomain.toCommRing.{u3} L (Field.toEuclideanDomain.{u3} L _inst_2)) (Field.isDomain.{u3} L _inst_2) _inst_5)) (AlgHom.range.{u1, u2, u3} F K L (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_4 (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_2))) _inst_5 f)) (Eq.{succ u2} (Subalgebra.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_4) (Algebra.adjoin.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_4 (Polynomial.rootSet.{u1, u2} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_3)) p K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) (Field.isDomain.{u2} K _inst_1) _inst_4)) (Top.top.{u2} (Subalgebra.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_4) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_4)))))
+Case conversion may be inaccurate. Consider using '#align polynomial.adjoin_root_set_eq_range Polynomial.adjoin_rootSet_eq_rangeₓ'. -/
 theorem adjoin_rootSet_eq_range [Algebra F K] [Algebra F L] {p : F[X]}
     (h : p.Splits (algebraMap F K)) (f : K →ₐ[F] L) :
     Algebra.adjoin F (p.rootSet L) = f.range ↔ Algebra.adjoin F (p.rootSet K) = ⊤ :=
@@ -349,6 +523,12 @@ theorem adjoin_rootSet_eq_range [Algebra F K] [Algebra F L] {p : F[X]}
   exact (Subalgebra.map_injective f.to_ring_hom.injective).eq_iff
 #align polynomial.adjoin_root_set_eq_range Polynomial.adjoin_rootSet_eq_range
 
+/- warning: polynomial.eq_prod_roots_of_splits -> Polynomial.eq_prod_roots_of_splits is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {p : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))} {i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i p) -> (Eq.{succ u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i p) (HMul.hMul.{u2, u2, u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (instHMul.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.mul'.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (fun (_x : RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) => L -> (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Polynomial.C.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (fun (_x : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) => K -> L) (RingHom.hasCoeToFun.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) i (Polynomial.leadingCoeff.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) p))) (Multiset.prod.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (CommRing.toCommMonoid.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.commRing.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)))) (Multiset.map.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (fun (a : L) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (instHSub.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.sub.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.X.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (fun (_x : RingHom.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) => L -> (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Polynomial.C.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) a)) (Polynomial.roots.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (Field.isDomain.{u2} L _inst_2) (Polynomial.map.{u1, u2} K L (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) i p))))))
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))} {i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))}, (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i p) -> (Eq.{succ u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i p) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p))) (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K 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+Case conversion may be inaccurate. Consider using '#align polynomial.eq_prod_roots_of_splits Polynomial.eq_prod_roots_of_splitsₓ'. -/
 theorem eq_prod_roots_of_splits {p : K[X]} {i : K →+* L} (hsplit : Splits i p) :
     p.map i = C (i p.leadingCoeff) * ((p.map i).roots.map fun a => X - C a).Prod :=
   by
@@ -357,11 +537,23 @@ theorem eq_prod_roots_of_splits {p : K[X]} {i : K →+* L} (hsplit : Splits i p)
   rw [nat_degree_map]; exact (nat_degree_eq_card_roots hsplit).symm
 #align polynomial.eq_prod_roots_of_splits Polynomial.eq_prod_roots_of_splits
 
+/- warning: polynomial.eq_prod_roots_of_splits_id -> Polynomial.eq_prod_roots_of_splits_id is a dubious translation:
+lean 3 declaration is
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K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.leadingCoeff.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) p)) (Multiset.prod.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.commRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)))) (Multiset.map.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (fun (a : K) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (instHSub.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.X.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (fun (_x : RingHom.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) => K -> (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} K (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.C.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) a)) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) p)))))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) p) -> (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) p (HMul.hMul.{u1, u1, u1} ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (instHMul.{u1} ((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_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Polynomial.mul'.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p)) (Multiset.prod.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (EuclideanDomain.toCommRing.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} K _inst_1))) (Multiset.map.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (fun (a : K) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) ((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_1)))) a) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) 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_1)))) _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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (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_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K 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(Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) a)) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) p)))))
+Case conversion may be inaccurate. Consider using '#align polynomial.eq_prod_roots_of_splits_id Polynomial.eq_prod_roots_of_splits_idₓ'. -/
 theorem eq_prod_roots_of_splits_id {p : K[X]} (hsplit : Splits (RingHom.id K) p) :
     p = C p.leadingCoeff * (p.roots.map fun a => X - C a).Prod := by
   simpa using eq_prod_roots_of_splits hsplit
 #align polynomial.eq_prod_roots_of_splits_id Polynomial.eq_prod_roots_of_splits_id
 
+/- warning: polynomial.eq_prod_roots_of_monic_of_splits_id -> Polynomial.eq_prod_roots_of_monic_of_splits_id is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) a)) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) p))))
+Case conversion may be inaccurate. Consider using '#align polynomial.eq_prod_roots_of_monic_of_splits_id Polynomial.eq_prod_roots_of_monic_of_splits_idₓ'. -/
 theorem eq_prod_roots_of_monic_of_splits_id {p : K[X]} (m : Monic p)
     (hsplit : Splits (RingHom.id K) p) : p = (p.roots.map fun a => X - C a).Prod :=
   by
@@ -369,14 +561,26 @@ theorem eq_prod_roots_of_monic_of_splits_id {p : K[X]} (m : Monic p)
   simp [m]
 #align polynomial.eq_prod_roots_of_monic_of_splits_id Polynomial.eq_prod_roots_of_monic_of_splits_id
 
-theorem eq_x_sub_c_of_splits_of_single_root {x : K} {h : K[X]} (h_splits : Splits i h)
+/- warning: polynomial.eq_X_sub_C_of_splits_of_single_root -> Polynomial.eq_X_sub_C_of_splits_of_single_root is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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_inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (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_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K 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(Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) x))))
+Case conversion may be inaccurate. Consider using '#align polynomial.eq_X_sub_C_of_splits_of_single_root Polynomial.eq_X_sub_C_of_splits_of_single_rootₓ'. -/
+theorem eq_X_sub_C_of_splits_of_single_root {x : K} {h : K[X]} (h_splits : Splits i h)
     (h_roots : (h.map i).roots = {i x}) : h = C h.leadingCoeff * (X - C x) :=
   by
   apply Polynomial.map_injective _ i.injective
   rw [eq_prod_roots_of_splits h_splits, h_roots]
   simp
-#align polynomial.eq_X_sub_C_of_splits_of_single_root Polynomial.eq_x_sub_c_of_splits_of_single_root
-
+#align polynomial.eq_X_sub_C_of_splits_of_single_root Polynomial.eq_X_sub_C_of_splits_of_single_root
+
+/- warning: polynomial.mem_lift_of_splits_of_roots_mem_range -> Polynomial.mem_lift_of_splits_of_roots_mem_range is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] (R : Type.{u2}) [_inst_4 : CommRing.{u2} R] [_inst_5 : Algebra.{u2, u1} R K (CommRing.toCommSemiring.{u2} R _inst_4) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))] {f : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) f) -> (Polynomial.Monic.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) f) -> (forall (a : K), (Membership.Mem.{u1, u1} K (Multiset.{u1} K) (Multiset.hasMem.{u1} K) a (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) f)) -> (Membership.Mem.{u1, u1} K (Subring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (SetLike.hasMem.{u1, u1} (Subring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) K (Subring.setLike.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) a (RingHom.range.{u2, u1} R K (CommRing.toRing.{u2} R _inst_4) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (algebraMap.{u2, u1} R K (CommRing.toCommSemiring.{u2} R _inst_4) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_5)))) -> (Membership.Mem.{u1, u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subsemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (SetLike.hasMem.{u1, u1} (Subsemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subsemiring.setLike.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Polynomial.semiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) f (Polynomial.lifts.{u2, u1} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (algebraMap.{u2, u1} R K (CommRing.toCommSemiring.{u2} R _inst_4) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_5)))
+but is expected to have type
+  forall {K : Type.{u2}} [_inst_1 : Field.{u2} K] (R : Type.{u1}) [_inst_4 : CommRing.{u1} R] [_inst_5 : Algebra.{u1, u2} R K (CommRing.toCommSemiring.{u1} R _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))] {f : Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))}, (Polynomial.Splits.{u2, u2} K K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) _inst_1 (RingHom.id.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1))))) f) -> (Polynomial.Monic.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) f) -> (forall (a : K), (Membership.mem.{u2, u2} K (Multiset.{u2} K) (Multiset.instMembershipMultiset.{u2} K) a (Polynomial.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) f)) -> (Membership.mem.{u2, u2} K (Subring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1))) (SetLike.instMembership.{u2, u2} (Subring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1))) K (Subring.instSetLikeSubring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))) a (RingHom.range.{u1, u2} R K (CommRing.toRing.{u1} R _inst_4) (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)) (algebraMap.{u1, u2} R K (CommRing.toCommSemiring.{u1} R _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_5)))) -> (Membership.mem.{u2, u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Subsemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))) f (Polynomial.lifts.{u1, u2} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (algebraMap.{u1, u2} R K (CommRing.toCommSemiring.{u1} R _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_5)))
+Case conversion may be inaccurate. Consider using '#align polynomial.mem_lift_of_splits_of_roots_mem_range Polynomial.mem_lift_of_splits_of_roots_mem_rangeₓ'. -/
 theorem mem_lift_of_splits_of_roots_mem_range (R : Type _) [CommRing R] [Algebra R K] {f : K[X]}
     (hs : f.Splits (RingHom.id K)) (hm : f.Monic) (hr : ∀ a ∈ f.roots, a ∈ (algebraMap R K).range) :
     f ∈ Polynomial.lifts (algebraMap R K) :=
@@ -396,6 +600,12 @@ local infixl:50 " ~ᵤ " => Associated
 
 open UniqueFactorizationMonoid Associates
 
+/- warning: polynomial.splits_of_exists_multiset -> Polynomial.splits_of_exists_multiset is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] (i : RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) {f : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))} {s : Multiset.{u2} L}, (Eq.{succ u2} (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Polynomial.map.{u1, u2} K L (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) i f) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f))) (Polynomial.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f))) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K (fun (a : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f))) (Polynomial.mul'.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K 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(Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => 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L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) a)) s)))) -> (Polynomial.Splits.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_2 i f)
+Case conversion may be inaccurate. Consider using '#align polynomial.splits_of_exists_multiset Polynomial.splits_of_exists_multisetₓ'. -/
 theorem splits_of_exists_multiset {f : K[X]} {s : Multiset L}
     (hs : f.map i = C (i f.leadingCoeff) * (s.map fun a : L => X - C a).Prod) : Splits i f :=
   if hf0 : f = 0 then hf0.symm ▸ splits_zero i
@@ -412,6 +622,7 @@ theorem splits_of_exists_multiset {f : K[X]} {s : Multiset L}
         exact degree_X_sub_C a
 #align polynomial.splits_of_exists_multiset Polynomial.splits_of_exists_multiset
 
+#print Polynomial.splits_of_splits_id /-
 theorem splits_of_splits_id {f : K[X]} : Splits (RingHom.id K) f → Splits i f :=
   UniqueFactorizationMonoid.induction_on_prime f (fun _ => splits_zero _)
     (fun _ hu _ => splits_of_degree_le_one _ ((isUnit_iff_degree_eq_zero.1 hu).symm ▸ by decide))
@@ -422,9 +633,16 @@ theorem splits_of_splits_id {f : K[X]} : Splits (RingHom.id K) f → Splits i f
           (by rw [map_id])))
       (ih (splits_of_splits_mul _ (mul_ne_zero hp.1 ha0) hfi).2)
 #align polynomial.splits_of_splits_id Polynomial.splits_of_splits_id
+-/
 
 end UFD
 
+/- warning: polynomial.splits_iff_exists_multiset -> Polynomial.splits_iff_exists_multiset is a dubious translation:
+lean 3 declaration is
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(Field.toDivisionRing.{u2} L _inst_2)))))) => L -> (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} L (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (Polynomial.semiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Polynomial.C.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) a)) s)))))
+but is expected to have type
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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => L) (Polynomial.leadingCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun 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+Case conversion may be inaccurate. Consider using '#align polynomial.splits_iff_exists_multiset Polynomial.splits_iff_exists_multisetₓ'. -/
 theorem splits_iff_exists_multiset {f : K[X]} :
     Splits i f ↔
       ∃ s : Multiset L, f.map i = C (i f.leadingCoeff) * (s.map fun a : L => X - C a).Prod :=
@@ -432,6 +650,7 @@ theorem splits_iff_exists_multiset {f : K[X]} :
     splits_of_exists_multiset i hs⟩
 #align polynomial.splits_iff_exists_multiset Polynomial.splits_iff_exists_multiset
 
+#print Polynomial.splits_comp_of_splits /-
 theorem splits_comp_of_splits (j : L →+* F) {f : K[X]} (h : Splits i f) : Splits (j.comp i) f :=
   by
   change i with (RingHom.id _).comp i at h
@@ -439,7 +658,14 @@ theorem splits_comp_of_splits (j : L →+* F) {f : K[X]} (h : Splits i f) : Spli
   rw [← splits_map_iff i] at h
   exact splits_of_splits_id _ h
 #align polynomial.splits_comp_of_splits Polynomial.splits_comp_of_splits
+-/
 
+/- warning: polynomial.splits_iff_card_roots -> Polynomial.splits_iff_card_roots is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, Iff (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) p) (Eq.{1} Nat (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.orderedCancelAddCommMonoid.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.orderedCancelAddCommMonoid.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} K) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.orderedCancelAddCommMonoid.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} K) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) p)) (Polynomial.natDegree.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) p))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, Iff (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) p) (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} K) => Nat) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) p)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} K) (fun (_x : Multiset.{u1} K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} K) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} K) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} K) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} K) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) p)) (Polynomial.natDegree.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) p))
+Case conversion may be inaccurate. Consider using '#align polynomial.splits_iff_card_roots Polynomial.splits_iff_card_rootsₓ'. -/
 /-- A polynomial splits if and only if it has as many roots as its degree. -/
 theorem splits_iff_card_roots {p : K[X]} : Splits (RingHom.id K) p ↔ p.roots.card = p.natDegree :=
   by
@@ -453,6 +679,7 @@ theorem splits_iff_card_roots {p : K[X]} : Splits (RingHom.id K) p ↔ p.roots.c
     exact (C_leading_coeff_mul_prod_multiset_X_sub_C hroots).symm
 #align polynomial.splits_iff_card_roots Polynomial.splits_iff_card_roots
 
+#print Polynomial.aeval_root_derivative_of_splits /-
 theorem aeval_root_derivative_of_splits [Algebra K L] {P : K[X]} (hmo : P.Monic)
     (hP : P.Splits (algebraMap K L)) {r : L} (hr : r ∈ (P.map (algebraMap K L)).roots) :
     aeval r P.derivative = (((P.map <| algebraMap K L).roots.eraseₓ r).map fun a => r - a).Prod :=
@@ -463,7 +690,14 @@ theorem aeval_root_derivative_of_splits [Algebra K L] {P : K[X]} (hmo : P.Monic)
   nth_rw 1 [eq_prod_roots_of_monic_of_splits_id hmo hP]
   rw [eval_multiset_prod_X_sub_C_derivative hr]
 #align polynomial.aeval_root_derivative_of_splits Polynomial.aeval_root_derivative_of_splits
+-/
 
+/- warning: polynomial.prod_roots_eq_coeff_zero_of_monic_of_split -> Polynomial.prod_roots_eq_coeff_zero_of_monic_of_split is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {P : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Polynomial.Monic.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) P) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) P) -> (Eq.{succ u1} K (Polynomial.coeff.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) P (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (Distrib.toHasMul.{u1} K (Ring.toDistrib.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (Ring.toMonoid.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (AddGroupWithOne.toAddGroup.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) (Polynomial.natDegree.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) P)) (Multiset.prod.{u1} K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) P))))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {P : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Monic.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) P) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) P) -> (Eq.{succ u1} K (Polynomial.coeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) P (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (HPow.hPow.{u1, 0, u1} K Nat K (instHPow.{u1, 0} K Nat (Monoid.Pow.{u1} K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Polynomial.natDegree.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) P)) (Multiset.prod.{u1} K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) P))))
+Case conversion may be inaccurate. Consider using '#align polynomial.prod_roots_eq_coeff_zero_of_monic_of_split Polynomial.prod_roots_eq_coeff_zero_of_monic_of_splitₓ'. -/
 /-- If `P` is a monic polynomial that splits, then `coeff P 0` equals the product of the roots. -/
 theorem prod_roots_eq_coeff_zero_of_monic_of_split {P : K[X]} (hmo : P.Monic)
     (hP : P.Splits (RingHom.id K)) : coeff P 0 = (-1) ^ P.natDegree * P.roots.Prod :=
@@ -480,6 +714,12 @@ theorem prod_roots_eq_coeff_zero_of_monic_of_split {P : K[X]} (hmo : P.Monic)
     splits_iff_card_roots.1 hP]
 #align polynomial.prod_roots_eq_coeff_zero_of_monic_of_split Polynomial.prod_roots_eq_coeff_zero_of_monic_of_split
 
+/- warning: polynomial.sum_roots_eq_next_coeff_of_monic_of_split -> Polynomial.sum_roots_eq_nextCoeff_of_monic_of_split is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {P : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))}, (Polynomial.Monic.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) P) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) P) -> (Eq.{succ u1} K (Polynomial.nextCoeff.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) P) (Neg.neg.{u1} K (SubNegMonoid.toHasNeg.{u1} K (AddGroup.toSubNegMonoid.{u1} K (AddGroupWithOne.toAddGroup.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Multiset.sum.{u1} K (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (Field.isDomain.{u1} K _inst_1) P))))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {P : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))}, (Polynomial.Monic.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) P) -> (Polynomial.Splits.{u1, u1} K K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) _inst_1 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) P) -> (Eq.{succ u1} K (Polynomial.nextCoeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) P) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Multiset.sum.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Polynomial.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) P))))
+Case conversion may be inaccurate. Consider using '#align polynomial.sum_roots_eq_next_coeff_of_monic_of_split Polynomial.sum_roots_eq_nextCoeff_of_monic_of_splitₓ'. -/
 /-- If `P` is a monic polynomial that splits, then `P.next_coeff` equals the sum of the roots. -/
 theorem sum_roots_eq_nextCoeff_of_monic_of_split {P : K[X]} (hmo : P.Monic)
     (hP : P.Splits (RingHom.id K)) : P.nextCoeff = -P.roots.Sum :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

@@ -330,7 +330,7 @@ theorem degree_eq_card_roots {p : K[X]} {i : K →+* L} (p_ne_zero : p ≠ 0) (h
 theorem roots_map {f : K[X]} (hf : f.Splits <| RingHom.id K) : (f.map i).roots = f.roots.map i :=
   (roots_map_of_injective_of_card_eq_natDegree i.Injective <|
       by
-      convert (nat_degree_eq_card_roots hf).symm
+      convert(nat_degree_eq_card_roots hf).symm
       rw [map_id]).symm
 #align polynomial.roots_map Polynomial.roots_map
 

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

@@ -179,7 +179,7 @@ theorem exists_root_of_splits' {f : K[X]} (hs : Splits i f) (hf0 : degree (f.map
         (show ¬IsUnit (f.map i) from mt isUnit_iff_degree_eq_zero.1 hf0) hf0'
     let ⟨x, hx⟩ := exists_root_of_degree_eq_one (hs.resolve_left hf0' hg.1 hg.2)
     let ⟨i, hi⟩ := hg.2
-    ⟨x, by rw [← eval_map, hi, eval_mul, show _ = _ from hx, zero_mul]⟩
+    ⟨x, by rw [← eval_map, hi, eval_mul, show _ = _ from hx, MulZeroClass.zero_mul]⟩
 #align polynomial.exists_root_of_splits' Polynomial.exists_root_of_splits'
 
 theorem roots_ne_zero_of_splits' {f : K[X]} (hs : Splits i f) (hf0 : natDegree (f.map i) ≠ 0) :
@@ -210,7 +210,7 @@ theorem natDegree_eq_card_roots' {p : K[X]} {i : K →+* L} (hsplit : Splits i p
   obtain ⟨q, he, hd, hr⟩ := exists_prod_multiset_X_sub_C_mul (p.map i)
   rw [← splits_id_iff_splits, ← he] at hsplit
   rw [← he] at hp
-  have hq : q ≠ 0 := fun h => hp (by rw [h, mul_zero])
+  have hq : q ≠ 0 := fun h => hp (by rw [h, MulZeroClass.mul_zero])
   rw [← hd, add_right_eq_self]
   by_contra
   have h' : (map (RingHom.id L) q).natDegree ≠ 0 := by simp [h]

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

@@ -78,7 +78,7 @@ theorem splits_of_map_eq_c {f : K[X]} {a : L} (h : f.map i = C a) : Splits i f :
 
 @[simp]
 theorem splits_c (a : K) : Splits i (C a) :=
-  splits_of_map_eq_c i (map_c i)
+  splits_of_map_eq_c i (map_C i)
 #align polynomial.splits_C Polynomial.splits_c
 
 theorem splits_of_map_degree_eq_one {f : K[X]} (hf : degree (f.map i) = 1) : Splits i f :=

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

@@ -141,11 +141,11 @@ theorem splits_of_isUnit [IsDomain K] {u : K[X]} (hu : IsUnit u) : u.Splits i :=
 #align polynomial.splits_of_is_unit Polynomial.splits_of_isUnit
 
 theorem splits_x_sub_c {x : K} : (X - C x).Splits i :=
-  splits_of_degree_le_one _ <| degree_x_sub_c_le _
+  splits_of_degree_le_one _ <| degree_X_sub_C_le _
 #align polynomial.splits_X_sub_C Polynomial.splits_x_sub_c
 
 theorem splits_x : X.Splits i :=
-  splits_of_degree_le_one _ degree_x_le
+  splits_of_degree_le_one _ degree_X_le
 #align polynomial.splits_X Polynomial.splits_x
 
 theorem splits_prod {ι : Type u} {s : ι → K[X]} {t : Finset ι} :

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

@@ -63,8 +63,8 @@ theorem splits_zero : Splits i (0 : K[X]) :=
   Or.inl (Polynomial.map_zero i)
 #align polynomial.splits_zero Polynomial.splits_zero
 
-theorem splits_of_map_eq_c {f : K[X]} {a : L} (h : f.map i = c a) : Splits i f :=
-  if ha : a = 0 then Or.inl (h.trans (ha.symm ▸ c_0))
+theorem splits_of_map_eq_c {f : K[X]} {a : L} (h : f.map i = C a) : Splits i f :=
+  if ha : a = 0 then Or.inl (h.trans (ha.symm ▸ C_0))
   else
     Or.inr fun g hg ⟨p, hp⟩ =>
       absurd hg.1 <|
@@ -77,7 +77,7 @@ theorem splits_of_map_eq_c {f : K[X]} {a : L} (h : f.map i = c a) : Splits i f :
 #align polynomial.splits_of_map_eq_C Polynomial.splits_of_map_eq_c
 
 @[simp]
-theorem splits_c (a : K) : Splits i (c a) :=
+theorem splits_c (a : K) : Splits i (C a) :=
   splits_of_map_eq_c i (map_c i)
 #align polynomial.splits_C Polynomial.splits_c
 
@@ -140,11 +140,11 @@ theorem splits_of_isUnit [IsDomain K] {u : K[X]} (hu : IsUnit u) : u.Splits i :=
   (isUnit_iff.mp hu).choose_spec.2 ▸ splits_c _ _
 #align polynomial.splits_of_is_unit Polynomial.splits_of_isUnit
 
-theorem splits_x_sub_c {x : K} : (x - c x).Splits i :=
+theorem splits_x_sub_c {x : K} : (X - C x).Splits i :=
   splits_of_degree_le_one _ <| degree_x_sub_c_le _
 #align polynomial.splits_X_sub_C Polynomial.splits_x_sub_c
 
-theorem splits_x : x.Splits i :=
+theorem splits_x : X.Splits i :=
   splits_of_degree_le_one _ degree_x_le
 #align polynomial.splits_X Polynomial.splits_x
 
@@ -162,7 +162,7 @@ theorem splits_pow {f : K[X]} (hf : f.Splits i) (n : ℕ) : (f ^ n).Splits i :=
   exact splits_prod i fun j hj => hf
 #align polynomial.splits_pow Polynomial.splits_pow
 
-theorem splits_x_pow (n : ℕ) : (x ^ n).Splits i :=
+theorem splits_x_pow (n : ℕ) : (X ^ n).Splits i :=
   splits_pow i (splits_x i) n
 #align polynomial.splits_X_pow Polynomial.splits_x_pow
 
@@ -350,7 +350,7 @@ theorem adjoin_rootSet_eq_range [Algebra F K] [Algebra F L] {p : F[X]}
 #align polynomial.adjoin_root_set_eq_range Polynomial.adjoin_rootSet_eq_range
 
 theorem eq_prod_roots_of_splits {p : K[X]} {i : K →+* L} (hsplit : Splits i p) :
-    p.map i = c (i p.leadingCoeff) * ((p.map i).roots.map fun a => x - c a).Prod :=
+    p.map i = C (i p.leadingCoeff) * ((p.map i).roots.map fun a => X - C a).Prod :=
   by
   rw [← leading_coeff_map]; symm
   apply C_leading_coeff_mul_prod_multiset_X_sub_C
@@ -358,19 +358,19 @@ theorem eq_prod_roots_of_splits {p : K[X]} {i : K →+* L} (hsplit : Splits i p)
 #align polynomial.eq_prod_roots_of_splits Polynomial.eq_prod_roots_of_splits
 
 theorem eq_prod_roots_of_splits_id {p : K[X]} (hsplit : Splits (RingHom.id K) p) :
-    p = c p.leadingCoeff * (p.roots.map fun a => x - c a).Prod := by
+    p = C p.leadingCoeff * (p.roots.map fun a => X - C a).Prod := by
   simpa using eq_prod_roots_of_splits hsplit
 #align polynomial.eq_prod_roots_of_splits_id Polynomial.eq_prod_roots_of_splits_id
 
 theorem eq_prod_roots_of_monic_of_splits_id {p : K[X]} (m : Monic p)
-    (hsplit : Splits (RingHom.id K) p) : p = (p.roots.map fun a => x - c a).Prod :=
+    (hsplit : Splits (RingHom.id K) p) : p = (p.roots.map fun a => X - C a).Prod :=
   by
   convert eq_prod_roots_of_splits_id hsplit
   simp [m]
 #align polynomial.eq_prod_roots_of_monic_of_splits_id Polynomial.eq_prod_roots_of_monic_of_splits_id
 
 theorem eq_x_sub_c_of_splits_of_single_root {x : K} {h : K[X]} (h_splits : Splits i h)
-    (h_roots : (h.map i).roots = {i x}) : h = c h.leadingCoeff * (x - c x) :=
+    (h_roots : (h.map i).roots = {i x}) : h = C h.leadingCoeff * (X - C x) :=
   by
   apply Polynomial.map_injective _ i.injective
   rw [eq_prod_roots_of_splits h_splits, h_roots]
@@ -397,7 +397,7 @@ local infixl:50 " ~ᵤ " => Associated
 open UniqueFactorizationMonoid Associates
 
 theorem splits_of_exists_multiset {f : K[X]} {s : Multiset L}
-    (hs : f.map i = c (i f.leadingCoeff) * (s.map fun a : L => x - c a).Prod) : Splits i f :=
+    (hs : f.map i = C (i f.leadingCoeff) * (s.map fun a : L => X - C a).Prod) : Splits i f :=
   if hf0 : f = 0 then hf0.symm ▸ splits_zero i
   else
     Or.inr fun p hp hdp => by
@@ -427,7 +427,7 @@ end UFD
 
 theorem splits_iff_exists_multiset {f : K[X]} :
     Splits i f ↔
-      ∃ s : Multiset L, f.map i = c (i f.leadingCoeff) * (s.map fun a : L => x - c a).Prod :=
+      ∃ s : Multiset L, f.map i = C (i f.leadingCoeff) * (s.map fun a : L => X - C a).Prod :=
   ⟨fun hf => ⟨(f.map i).roots, eq_prod_roots_of_splits hf⟩, fun ⟨s, hs⟩ =>
     splits_of_exists_multiset i hs⟩
 #align polynomial.splits_iff_exists_multiset Polynomial.splits_iff_exists_multiset

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

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

@@ -233,12 +233,10 @@ theorem splits_iff (f : K[X]) :
 #align polynomial.splits_iff Polynomial.splits_iff
 
 /-- This lemma is for polynomials over a field. -/
--- Adaptation note: 2024-03-15
--- Renamed to avoid the reserved name `Splits.def`.
-theorem Splits.def' {i : K →+* L} {f : K[X]} (h : Splits i f) :
+theorem Splits.def {i : K →+* L} {f : K[X]} (h : Splits i f) :
     f = 0 ∨ ∀ {g : L[X]}, Irreducible g → g ∣ f.map i → degree g = 1 :=
   (splits_iff i f).mp h
-#align polynomial.splits.def Polynomial.Splits.def'
+#align polynomial.splits.def Polynomial.Splits.def
 
 theorem splits_of_splits_mul {f g : K[X]} (hfg : f * g ≠ 0) (h : Splits i (f * g)) :
     Splits i f ∧ Splits i g :=
@@ -411,7 +409,7 @@ theorem splits_of_splits_id {f : K[X]} : Splits (RingHom.id K) f → Splits i f
     fun a p ha0 hp ih hfi =>
     splits_mul _
       (splits_of_degree_eq_one _
-        ((splits_of_splits_mul _ (mul_ne_zero hp.1 ha0) hfi).1.def'.resolve_left hp.1 hp.irreducible
+        ((splits_of_splits_mul _ (mul_ne_zero hp.1 ha0) hfi).1.def.resolve_left hp.1 hp.irreducible
           (by rw [map_id])))
       (ih (splits_of_splits_mul _ (mul_ne_zero hp.1 ha0) hfi).2)
 #align polynomial.splits_of_splits_id Polynomial.splits_of_splits_id

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

@@ -3,9 +3,9 @@ Copyright (c) 2018 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 -/
+import Mathlib.Algebra.Polynomial.FieldDivision
+import Mathlib.Algebra.Polynomial.Lifts
 import Mathlib.Data.List.Prime
-import Mathlib.Data.Polynomial.FieldDivision
-import Mathlib.Data.Polynomial.Lifts
 
 #align_import data.polynomial.splits from "leanprover-community/mathlib"@"f694c7dead66f5d4c80f446c796a5aad14707f0e"
 

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

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

@@ -233,10 +233,12 @@ theorem splits_iff (f : K[X]) :
 #align polynomial.splits_iff Polynomial.splits_iff
 
 /-- This lemma is for polynomials over a field. -/
-theorem Splits.def {i : K →+* L} {f : K[X]} (h : Splits i f) :
+-- Adaptation note: 2024-03-15
+-- Renamed to avoid the reserved name `Splits.def`.
+theorem Splits.def' {i : K →+* L} {f : K[X]} (h : Splits i f) :
     f = 0 ∨ ∀ {g : L[X]}, Irreducible g → g ∣ f.map i → degree g = 1 :=
   (splits_iff i f).mp h
-#align polynomial.splits.def Polynomial.Splits.def
+#align polynomial.splits.def Polynomial.Splits.def'
 
 theorem splits_of_splits_mul {f g : K[X]} (hfg : f * g ≠ 0) (h : Splits i (f * g)) :
     Splits i f ∧ Splits i g :=
@@ -409,7 +411,7 @@ theorem splits_of_splits_id {f : K[X]} : Splits (RingHom.id K) f → Splits i f
     fun a p ha0 hp ih hfi =>
     splits_mul _
       (splits_of_degree_eq_one _
-        ((splits_of_splits_mul _ (mul_ne_zero hp.1 ha0) hfi).1.def.resolve_left hp.1 hp.irreducible
+        ((splits_of_splits_mul _ (mul_ne_zero hp.1 ha0) hfi).1.def'.resolve_left hp.1 hp.irreducible
           (by rw [map_id])))
       (ih (splits_of_splits_mul _ (mul_ne_zero hp.1 ha0) hfi).2)
 #align polynomial.splits_of_splits_id Polynomial.splits_of_splits_id

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

@@ -41,7 +41,6 @@ section Splits
 section CommRing
 
 variable [CommRing K] [Field L] [Field F]
-
 variable (i : K →+* L)
 
 /-- A polynomial `Splits` iff it is zero or all of its irreducible factors have `degree` 1. -/
@@ -225,7 +224,6 @@ theorem degree_eq_card_roots' {p : K[X]} {i : K →+* L} (p_ne_zero : p.map i 
 end CommRing
 
 variable [CommRing R] [Field K] [Field L] [Field F]
-
 variable (i : K →+* L)
 
 /-- This lemma is for polynomials over a field. -/

• Introduce typeclass DecompositionMonoid, which says every element in the monoid is primal, i.e., whenever an element divides a product b * c, it can be factored into a product such that the factors divides b and c respectively. A domain is called pre-Schreier if its multiplicative monoid is a decomposition monoid, and these are more general than GCD domains.

• Show that any GCDMonoid is a DecompositionMonoid. In order for lemmas about DecompositionMonoids to automatically apply to UniqueFactorizationMonoids, we add instances from UniqueFactorizationMonoid α to Nonempty (NormalizedGCDMonoid α) to Nonempty (GCDMonoid α) to DecompositionMonoid α. (Zulip) See the bottom of message for an updated diagram of classes and instances.

• Introduce binary predicate IsRelPrime which says that the only common divisors of the two elements are units. Replace previous occurrences in mathlib by this predicate.

• Duplicate all lemmas about IsCoprime in Coprime/Basic (except three lemmas about smul) to IsRelPrime. Due to import constraints, they are spread into three files Algebra/Divisibility/Units (including key lemmas assuming DecompositionMonoid), GroupWithZero/Divisibility, and Coprime/Basic.

• Show IsCoprime always imply IsRelPrime and is equivalent to it in Bezout rings. To reduce duplication, the definition of Bezout rings and the GCDMonoid instance are moved from RingTheory/Bezout to RingTheory/PrincipalIdealDomain, and some results in PrincipalIdealDomain are generalized to Bezout rings.

• Remove the recently added file Squarefree/UniqueFactorizationMonoid and place the results appropriately within Squarefree/Basic. All results are generalized to DecompositionMonoid or weaker except the last one.

Zulip

With this PR, all the following instances (indicated by arrows) now work; this PR fills the central part.

                                                                          EuclideanDomain (bundled)
                                                                              ↙          ↖
                                                                 IsPrincipalIdealRing ← Field (bundled)
                                                                            ↓             ↓
         NormalizationMonoid ←          NormalizedGCDMonoid → GCDMonoid  IsBezout ← ValuationRing ← DiscreteValuationRing
                   ↓                             ↓                 ↘       ↙
Nonempty NormalizationMonoid ← Nonempty NormalizedGCDMonoid →  Nonempty GCDMonoid → IsIntegrallyClosed
                                                 ↑                    ↓
                    WfDvdMonoid ← UniqueFactorizationMonoid → DecompositionMonoid
                                                 ↑
                                       IsPrincipalIdealRing

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com> Co-authored-by: Oliver Nash <github@olivernash.org>

@@ -108,7 +108,7 @@ theorem splits_mul {f g : K[X]} (hf : Splits i f) (hg : Splits i g) : Splits i (
   if h : (f * g).map i = 0 then Or.inl h
   else
     Or.inr @fun p hp hpf =>
-      ((PrincipalIdealRing.irreducible_iff_prime.1 hp).2.2 _ _
+      ((irreducible_iff_prime.1 hp).2.2 _ _
             (show p ∣ map i f * map i g by convert hpf; rw [Polynomial.map_mul])).elim
         (hf.resolve_left (fun hf => by simp [hf] at h) hp)
         (hg.resolve_left (fun hg => by simp [hg] at h) hp)

• generalize image_rootSet, adjoin_rootSet_eq_range and splits_comp_of_splits in Data/Polynomial/Splits and use the last one to golf splits_of_algHom, splits_of_isScalarTower (introduced in # 8609).

• add three new lemmas mem_range_x_of_minpoly_splits to simplify the construction of IntermediateField.algHomEquivAlgHomOfIsAlgClosed and Algebra.IsAlgebraic.algHomEquivAlgHomOfIsAlgClosed, remove the IsAlgClosed condition and rename. They could be moved to an earlier file but I refrain from doing that. (#find_home says it's already in the right place)

• golf primitive_element_iff_algHom_eq_of_eval from # 8609, using a new lemma IsIntegral.minpoly_splits_tower_top for the last step.

• make integralClosure_algEquiv_restrict (from # 8714) computable and rename to AlgEquiv.mapIntegralClosure to follow camelCase naming convention and enable dot notation.

Co-authored-by: Xavier-François Roblot <46200072+xroblot@users.noreply.github.com> Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

@@ -30,7 +30,7 @@ open BigOperators Polynomial
 
 universe u v w
 
-variable {F : Type u} {K : Type v} {L : Type w}
+variable {R : Type*} {F : Type u} {K : Type v} {L : Type w}
 
 namespace Polynomial
 
@@ -224,7 +224,7 @@ theorem degree_eq_card_roots' {p : K[X]} {i : K →+* L} (p_ne_zero : p.map i 
 
 end CommRing
 
-variable [Field K] [Field L] [Field F]
+variable [CommRing R] [Field K] [Field L] [Field F]
 
 variable (i : K →+* L)
 
@@ -329,17 +329,17 @@ theorem roots_map {f : K[X]} (hf : f.Splits <| RingHom.id K) : (f.map i).roots =
       rw [map_id]).symm
 #align polynomial.roots_map Polynomial.roots_map
 
-theorem image_rootSet [Algebra F K] [Algebra F L] {p : F[X]} (h : p.Splits (algebraMap F K))
-    (f : K →ₐ[F] L) : f '' p.rootSet K = p.rootSet L := by
+theorem image_rootSet [Algebra R K] [Algebra R L] {p : R[X]} (h : p.Splits (algebraMap R K))
+    (f : K →ₐ[R] L) : f '' p.rootSet K = p.rootSet L := by
   classical
     rw [rootSet, ← Finset.coe_image, ← Multiset.toFinset_map, ← f.coe_toRingHom,
-      ← roots_map _ ((splits_id_iff_splits (algebraMap F K)).mpr h), map_map, f.comp_algebraMap,
+      ← roots_map _ ((splits_id_iff_splits (algebraMap R K)).mpr h), map_map, f.comp_algebraMap,
       ← rootSet]
 #align polynomial.image_root_set Polynomial.image_rootSet
 
-theorem adjoin_rootSet_eq_range [Algebra F K] [Algebra F L] {p : F[X]}
-    (h : p.Splits (algebraMap F K)) (f : K →ₐ[F] L) :
-    Algebra.adjoin F (p.rootSet L) = f.range ↔ Algebra.adjoin F (p.rootSet K) = ⊤ := by
+theorem adjoin_rootSet_eq_range [Algebra R K] [Algebra R L] {p : R[X]}
+    (h : p.Splits (algebraMap R K)) (f : K →ₐ[R] L) :
+    Algebra.adjoin R (p.rootSet L) = f.range ↔ Algebra.adjoin R (p.rootSet K) = ⊤ := by
   rw [← image_rootSet h f, Algebra.adjoin_image, ← Algebra.map_top]
   exact (Subalgebra.map_injective f.toRingHom.injective).eq_iff
 #align polynomial.adjoin_root_set_eq_range Polynomial.adjoin_rootSet_eq_range
@@ -370,7 +370,8 @@ theorem eq_X_sub_C_of_splits_of_single_root {x : K} {h : K[X]} (h_splits : Split
 set_option linter.uppercaseLean3 false in
 #align polynomial.eq_X_sub_C_of_splits_of_single_root Polynomial.eq_X_sub_C_of_splits_of_single_root
 
-theorem mem_lift_of_splits_of_roots_mem_range (R : Type*) [CommRing R] [Algebra R K] {f : K[X]}
+variable (R) in
+theorem mem_lift_of_splits_of_roots_mem_range [Algebra R K] {f : K[X]}
     (hs : f.Splits (RingHom.id K)) (hm : f.Monic) (hr : ∀ a ∈ f.roots, a ∈ (algebraMap R K).range) :
     f ∈ Polynomial.lifts (algebraMap R K) := by
   rw [eq_prod_roots_of_monic_of_splits_id hm hs, lifts_iff_liftsRing]
@@ -438,27 +439,22 @@ theorem splits_id_of_splits {f : K[X]} (h : Splits i f)
     (roots_mem_range : ∀ a ∈ (f.map i).roots, a ∈ i.range) : Splits (RingHom.id K) f :=
   splits_of_comp (RingHom.id K) i h roots_mem_range
 
-theorem splits_of_algHom {R L' : Type*} [CommRing R] [Field L'] [Algebra R L] [Algebra R L']
-    {f : R[X]} (h : Polynomial.Splits (algebraMap R L) f) (e : L →ₐ[R] L') :
-    Polynomial.Splits (algebraMap R L') f := by
-  rw [← splits_id_iff_splits, ← AlgHom.comp_algebraMap_of_tower R e, ← map_map,
-    splits_id_iff_splits]
-  exact splits_of_splits_id e.toRingHom <| (splits_id_iff_splits _).mpr h
-
-theorem splits_of_isScalarTower {R : Type*} (L' : Type*) [CommRing R] [Field L'] [Algebra R L]
-    [Algebra R L'] [Algebra L L'] [IsScalarTower R L L'] {f : R[X]}
-    (h : Polynomial.Splits (algebraMap R L) f) :
-    Polynomial.Splits (algebraMap R L') f :=
-  splits_of_algHom h (IsScalarTower.toAlgHom R L L')
-
-theorem splits_comp_of_splits (j : L →+* F) {f : K[X]} (h : Splits i f) : Splits (j.comp i) f := by
-  -- Porting note: was
-  -- change i with (RingHom.id _).comp i at h
-  rw [← splits_map_iff]
-  rw [← RingHom.id_comp i, ← splits_map_iff i] at h
-  exact splits_of_splits_id _ h
+theorem splits_comp_of_splits (i : R →+* K) (j : K →+* L) {f : R[X]} (h : Splits i f) :
+    Splits (j.comp i) f :=
+  (splits_map_iff i j).mp (splits_of_splits_id _ <| (splits_map_iff i <| .id K).mpr h)
 #align polynomial.splits_comp_of_splits Polynomial.splits_comp_of_splits
 
+variable [Algebra R K] [Algebra R L]
+
+theorem splits_of_algHom {f : R[X]} (h : Splits (algebraMap R K) f) (e : K →ₐ[R] L) :
+    Splits (algebraMap R L) f := by
+  rw [← e.comp_algebraMap_of_tower R]; exact splits_comp_of_splits _ _ h
+
+variable (L) in
+theorem splits_of_isScalarTower {f : R[X]} [Algebra K L] [IsScalarTower R K L]
+    (h : Splits (algebraMap R K) f) : Splits (algebraMap R L) f :=
+  splits_of_algHom h (IsScalarTower.toAlgHom R K L)
+
 /-- A polynomial splits if and only if it has as many roots as its degree. -/
 theorem splits_iff_card_roots {p : K[X]} :
     Splits (RingHom.id K) p ↔ Multiset.card p.roots = p.natDegree := by

See the Zulip thread

@@ -438,6 +438,19 @@ theorem splits_id_of_splits {f : K[X]} (h : Splits i f)
     (roots_mem_range : ∀ a ∈ (f.map i).roots, a ∈ i.range) : Splits (RingHom.id K) f :=
   splits_of_comp (RingHom.id K) i h roots_mem_range
 
+theorem splits_of_algHom {R L' : Type*} [CommRing R] [Field L'] [Algebra R L] [Algebra R L']
+    {f : R[X]} (h : Polynomial.Splits (algebraMap R L) f) (e : L →ₐ[R] L') :
+    Polynomial.Splits (algebraMap R L') f := by
+  rw [← splits_id_iff_splits, ← AlgHom.comp_algebraMap_of_tower R e, ← map_map,
+    splits_id_iff_splits]
+  exact splits_of_splits_id e.toRingHom <| (splits_id_iff_splits _).mpr h
+
+theorem splits_of_isScalarTower {R : Type*} (L' : Type*) [CommRing R] [Field L'] [Algebra R L]
+    [Algebra R L'] [Algebra L L'] [IsScalarTower R L L'] {f : R[X]}
+    (h : Polynomial.Splits (algebraMap R L) f) :
+    Polynomial.Splits (algebraMap R L') f :=
+  splits_of_algHom h (IsScalarTower.toAlgHom R L L')
+
 theorem splits_comp_of_splits (j : L →+* F) {f : K[X]} (h : Splits i f) : Splits (j.comp i) f := by
   -- Porting note: was
   -- change i with (RingHom.id _).comp i at h

Before: Construction only imports Normal, which transitively imports IsSplittingField Now: Normal imports Construction, Construction only imports IsSplittingField So no extra transitive import is added to any file other than Construction and Normal. As a consequence, Polynomial.SplittingField.instNormal is moved from Construction to Normal.

adjoin_rootSet_eq_range is added to IsSplittingField.

splits_of_comp in Splits is extracted from splits_of_splits in IsSplittingField.

Source of proof: https://math.stackexchange.com/a/2585087/12932

Move Algebra.adjoin.liftSingleton from IsAlgClosed/Basic to Adjoin/Field in order to speed up lift_of_splits (renamed to add namespace Polynomial).

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

@@ -21,12 +21,6 @@ irreducible factors over `L` have degree `1`.
   field and a polynomial `f` saying that `f.map i` is zero or all of its irreducible factors over
   `L` have degree `1`.
 
-## Main statements
-
-* `lift_of_splits`: If `K` and `L` are field extensions of a field `F` and for some finite subset
-  `S` of `K`, the minimal polynomial of every `x ∈ K` splits as a polynomial with coefficients in
-  `L`, then `Algebra.adjoin F S` embeds into `L`.
-
 -/
 
 
@@ -430,6 +424,20 @@ theorem splits_iff_exists_multiset {f : K[X]} :
     splits_of_exists_multiset i hs⟩
 #align polynomial.splits_iff_exists_multiset Polynomial.splits_iff_exists_multiset
 
+theorem splits_of_comp (j : L →+* F) {f : K[X]} (h : Splits (j.comp i) f)
+    (roots_mem_range : ∀ a ∈ (f.map (j.comp i)).roots, a ∈ j.range) : Splits i f := by
+  choose lift lift_eq using roots_mem_range
+  rw [splits_iff_exists_multiset]
+  refine ⟨(f.map (j.comp i)).roots.pmap lift fun _ ↦ id, map_injective _ j.injective ?_⟩
+  conv_lhs => rw [Polynomial.map_map, eq_prod_roots_of_splits h]
+  simp_rw [Polynomial.map_mul, Polynomial.map_multiset_prod, Multiset.map_pmap, Polynomial.map_sub,
+    map_C, map_X, lift_eq, Multiset.pmap_eq_map]
+  rfl
+
+theorem splits_id_of_splits {f : K[X]} (h : Splits i f)
+    (roots_mem_range : ∀ a ∈ (f.map i).roots, a ∈ i.range) : Splits (RingHom.id K) f :=
+  splits_of_comp (RingHom.id K) i h roots_mem_range
+
 theorem splits_comp_of_splits (j : L →+* F) {f : K[X]} (h : Splits i f) : Splits (j.comp i) f := by
   -- Porting note: was
   -- change i with (RingHom.id _).comp i at h

Replace rcases( with rcases (. Same thing for convert( and congrm(. No other change.

@@ -331,7 +331,7 @@ theorem degree_eq_card_roots {p : K[X]} {i : K →+* L} (p_ne_zero : p ≠ 0) (h
 
 theorem roots_map {f : K[X]} (hf : f.Splits <| RingHom.id K) : (f.map i).roots = f.roots.map i :=
   (roots_map_of_injective_of_card_eq_natDegree i.injective <| by
-      convert(natDegree_eq_card_roots hf).symm
+      convert (natDegree_eq_card_roots hf).symm
       rw [map_id]).symm
 #align polynomial.roots_map Polynomial.roots_map
 

These make the lemmas strictly more (syntactically) general.

As usual, the way to find these is to remove open Classical and fix what breaks. Usually this means adding classical to the start of the proof, but there are lots of weird term-mode proofs here for which adding a more surgical letI := Classical.decEq is easier.

@@ -32,7 +32,7 @@ irreducible factors over `L` have degree `1`.
 
 noncomputable section
 
-open Classical BigOperators Polynomial
+open BigOperators Polynomial
 
 universe u v w
 
@@ -61,6 +61,7 @@ theorem splits_zero : Splits i (0 : K[X]) :=
 #align polynomial.splits_zero Polynomial.splits_zero
 
 theorem splits_of_map_eq_C {f : K[X]} {a : L} (h : f.map i = C a) : Splits i f :=
+  letI := Classical.decEq L
   if ha : a = 0 then Or.inl (h.trans (ha.symm ▸ C_0))
   else
     Or.inr fun hg ⟨p, hp⟩ =>
@@ -109,6 +110,7 @@ theorem splits_of_natDegree_eq_one {f : K[X]} (hf : natDegree f = 1) : Splits i
 #align polynomial.splits_of_nat_degree_eq_one Polynomial.splits_of_natDegree_eq_one
 
 theorem splits_mul {f g : K[X]} (hf : Splits i f) (hg : Splits i g) : Splits i (f * g) :=
+  letI := Classical.decEq L
   if h : (f * g).map i = 0 then Or.inl h
   else
     Or.inr @fun p hp hpf =>
@@ -150,6 +152,7 @@ set_option linter.uppercaseLean3 false in
 
 theorem splits_prod {ι : Type u} {s : ι → K[X]} {t : Finset ι} :
     (∀ j ∈ t, (s j).Splits i) → (∏ x in t, s x).Splits i := by
+  classical
   refine' Finset.induction_on t (fun _ => splits_one i) fun a t hat ih ht => _
   rw [Finset.forall_mem_insert] at ht; rw [Finset.prod_insert hat]
   exact splits_mul i ht.1 (ih ht.2)
@@ -171,6 +174,7 @@ theorem splits_id_iff_splits {f : K[X]} : (f.map i).Splits (RingHom.id L) ↔ f.
 
 theorem exists_root_of_splits' {f : K[X]} (hs : Splits i f) (hf0 : degree (f.map i) ≠ 0) :
     ∃ x, eval₂ i x f = 0 :=
+  letI := Classical.decEq L
   if hf0' : f.map i = 0 then by simp [eval₂_eq_eval_map, hf0']
   else
     let ⟨g, hg⟩ :=
@@ -253,12 +257,12 @@ theorem splits_of_splits_of_dvd {f g : K[X]} (hf0 : f ≠ 0) (hf : Splits i f) (
   exact (splits_of_splits_mul i hf0 hf).1
 #align polynomial.splits_of_splits_of_dvd Polynomial.splits_of_splits_of_dvd
 
-theorem splits_of_splits_gcd_left {f g : K[X]} (hf0 : f ≠ 0) (hf : Splits i f) :
+theorem splits_of_splits_gcd_left [DecidableEq K] {f g : K[X]} (hf0 : f ≠ 0) (hf : Splits i f) :
     Splits i (EuclideanDomain.gcd f g) :=
   Polynomial.splits_of_splits_of_dvd i hf0 hf (EuclideanDomain.gcd_dvd_left f g)
 #align polynomial.splits_of_splits_gcd_left Polynomial.splits_of_splits_gcd_left
 
-theorem splits_of_splits_gcd_right {f g : K[X]} (hg0 : g ≠ 0) (hg : Splits i g) :
+theorem splits_of_splits_gcd_right [DecidableEq K] {f g : K[X]} (hg0 : g ≠ 0) (hg : Splits i g) :
     Splits i (EuclideanDomain.gcd f g) :=
   Polynomial.splits_of_splits_of_dvd i hg0 hg (EuclideanDomain.gcd_dvd_right f g)
 #align polynomial.splits_of_splits_gcd_right Polynomial.splits_of_splits_gcd_right
@@ -270,6 +274,7 @@ theorem splits_mul_iff {f g : K[X]} (hf : f ≠ 0) (hg : g ≠ 0) :
 
 theorem splits_prod_iff {ι : Type u} {s : ι → K[X]} {t : Finset ι} :
     (∀ j ∈ t, s j ≠ 0) → ((∏ x in t, s x).Splits i ↔ ∀ j ∈ t, (s j).Splits i) := by
+  classical
   refine'
     Finset.induction_on t (fun _ =>
         ⟨fun _ _ h => by simp only [Finset.not_mem_empty] at h, fun _ => splits_one i⟩)
@@ -390,6 +395,7 @@ open UniqueFactorizationMonoid Associates
 
 theorem splits_of_exists_multiset {f : K[X]} {s : Multiset L}
     (hs : f.map i = C (i f.leadingCoeff) * (s.map fun a : L => X - C a).prod) : Splits i f :=
+  letI := Classical.decEq K
   if hf0 : f = 0 then hf0.symm ▸ splits_zero i
   else
     Or.inr @fun p hp hdp => by
@@ -445,7 +451,7 @@ theorem splits_iff_card_roots {p : K[X]} :
     exact (C_leadingCoeff_mul_prod_multiset_X_sub_C hroots).symm
 #align polynomial.splits_iff_card_roots Polynomial.splits_iff_card_roots
 
-theorem aeval_root_derivative_of_splits [Algebra K L] {P : K[X]} (hmo : P.Monic)
+theorem aeval_root_derivative_of_splits [Algebra K L] [DecidableEq L] {P : K[X]} (hmo : P.Monic)
     (hP : P.Splits (algebraMap K L)) {r : L} (hr : r ∈ P.aroots L) :
     aeval r (Polynomial.derivative P) =
     (((P.aroots L).erase r).map fun a => r - a).prod := by

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

@@ -446,9 +446,9 @@ theorem splits_iff_card_roots {p : K[X]} :
 #align polynomial.splits_iff_card_roots Polynomial.splits_iff_card_roots
 
 theorem aeval_root_derivative_of_splits [Algebra K L] {P : K[X]} (hmo : P.Monic)
-    (hP : P.Splits (algebraMap K L)) {r : L} (hr : r ∈ (P.map (algebraMap K L)).roots) :
+    (hP : P.Splits (algebraMap K L)) {r : L} (hr : r ∈ P.aroots L) :
     aeval r (Polynomial.derivative P) =
-    (((P.map <| algebraMap K L).roots.erase r).map fun a => r - a).prod := by
+    (((P.aroots L).erase r).map fun a => r - a).prod := by
   replace hmo := hmo.map (algebraMap K L)
   replace hP := (splits_id_iff_splits (algebraMap K L)).2 hP
   rw [aeval_def, ← eval_map, ← derivative_map]

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).

@@ -178,7 +178,7 @@ theorem exists_root_of_splits' {f : K[X]} (hs : Splits i f) (hf0 : degree (f.map
         (show ¬IsUnit (f.map i) from mt isUnit_iff_degree_eq_zero.1 hf0) hf0'
     let ⟨x, hx⟩ := exists_root_of_degree_eq_one (hs.resolve_left hf0' hg.1 hg.2)
     let ⟨i, hi⟩ := hg.2
-    ⟨x, by rw [← eval_map, hi, eval_mul, show _ = _ from hx, MulZeroClass.zero_mul]⟩
+    ⟨x, by rw [← eval_map, hi, eval_mul, show _ = _ from hx, zero_mul]⟩
 #align polynomial.exists_root_of_splits' Polynomial.exists_root_of_splits'
 
 theorem roots_ne_zero_of_splits' {f : K[X]} (hs : Splits i f) (hf0 : natDegree (f.map i) ≠ 0) :
@@ -208,7 +208,7 @@ theorem natDegree_eq_card_roots' {p : K[X]} {i : K →+* L} (hsplit : Splits i p
   obtain ⟨q, he, hd, hr⟩ := exists_prod_multiset_X_sub_C_mul (p.map i)
   rw [← splits_id_iff_splits, ← he] at hsplit
   rw [← he] at hp
-  have hq : q ≠ 0 := fun h => hp (by rw [h, MulZeroClass.mul_zero])
+  have hq : q ≠ 0 := fun h => hp (by rw [h, mul_zero])
   rw [← hd, add_right_eq_self]
   by_contra h
   have h' : (map (RingHom.id L) q).natDegree ≠ 0 := by simp [h]

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

This has nice performance benefits.

@@ -371,7 +371,7 @@ theorem eq_X_sub_C_of_splits_of_single_root {x : K} {h : K[X]} (h_splits : Split
 set_option linter.uppercaseLean3 false in
 #align polynomial.eq_X_sub_C_of_splits_of_single_root Polynomial.eq_X_sub_C_of_splits_of_single_root
 
-theorem mem_lift_of_splits_of_roots_mem_range (R : Type _) [CommRing R] [Algebra R K] {f : K[X]}
+theorem mem_lift_of_splits_of_roots_mem_range (R : Type*) [CommRing R] [Algebra R K] {f : K[X]}
     (hs : f.Splits (RingHom.id K)) (hm : f.Monic) (hr : ∀ a ∈ f.roots, a ∈ (algebraMap R K).range) :
     f ∈ Polynomial.lifts (algebraMap R K) := by
   rw [eq_prod_roots_of_monic_of_splits_id hm hs, lifts_iff_liftsRing]

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2018 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
-
-! This file was ported from Lean 3 source module data.polynomial.splits
-! leanprover-community/mathlib commit f694c7dead66f5d4c80f446c796a5aad14707f0e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.List.Prime
 import Mathlib.Data.Polynomial.FieldDivision
 import Mathlib.Data.Polynomial.Lifts
 
+#align_import data.polynomial.splits from "leanprover-community/mathlib"@"f694c7dead66f5d4c80f446c796a5aad14707f0e"
+
 /-!
 # Split polynomials
 

Changes are of the form

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

@@ -277,7 +277,7 @@ theorem splits_prod_iff {ι : Type u} {s : ι → K[X]} {t : Finset ι} :
     Finset.induction_on t (fun _ =>
         ⟨fun _ _ h => by simp only [Finset.not_mem_empty] at h, fun _ => splits_one i⟩)
       fun a t hat ih ht => _
-  rw [Finset.forall_mem_insert] at ht⊢
+  rw [Finset.forall_mem_insert] at ht ⊢
   rw [Finset.prod_insert hat, splits_mul_iff i ht.1 (Finset.prod_ne_zero_iff.2 ht.2), ih ht.2]
 #align polynomial.splits_prod_iff Polynomial.splits_prod_iff
 

@@ -91,7 +91,6 @@ theorem splits_of_map_degree_eq_one {f : K[X]} (hf : degree (f.map i) = 1) : Spl
     tauto
 #align polynomial.splits_of_map_degree_eq_one Polynomial.splits_of_map_degree_eq_one
 
-attribute [-instance] Ring.toNonAssocRing in -- Porting note: gets around lean4#2074
 theorem splits_of_degree_le_one {f : K[X]} (hf : degree f ≤ 1) : Splits i f :=
   if hif : degree (f.map i) ≤ 0 then splits_of_map_eq_C i (degree_le_zero_iff.mp hif)
   else by

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

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

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

@@ -112,9 +112,6 @@ theorem splits_of_natDegree_eq_one {f : K[X]} (hf : natDegree f = 1) : Splits i
   splits_of_natDegree_le_one i (le_of_eq hf)
 #align polynomial.splits_of_nat_degree_eq_one Polynomial.splits_of_natDegree_eq_one
 
-set_option synthInstance.etaExperiment true in
-set_option synthInstance.maxHeartbeats 100000 in
-set_option maxHeartbeats 300000 in
 theorem splits_mul {f g : K[X]} (hf : Splits i f) (hg : Splits i g) : Splits i (f * g) :=
   if h : (f * g).map i = 0 then Or.inl h
   else
@@ -176,8 +173,6 @@ theorem splits_id_iff_splits {f : K[X]} : (f.map i).Splits (RingHom.id L) ↔ f.
   rw [splits_map_iff, RingHom.id_comp]
 #align polynomial.splits_id_iff_splits Polynomial.splits_id_iff_splits
 
-set_option synthInstance.maxHeartbeats 100000 in
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem exists_root_of_splits' {f : K[X]} (hs : Splits i f) (hf0 : degree (f.map i) ≠ 0) :
     ∃ x, eval₂ i x f = 0 :=
   if hf0' : f.map i = 0 then by simp [eval₂_eq_eval_map, hf0']
@@ -210,7 +205,6 @@ theorem map_rootOfSplits' {f : K[X]} (hf : f.Splits i) (hfd) :
   Classical.choose_spec <| exists_root_of_splits' i hf hfd
 #align polynomial.map_root_of_splits' Polynomial.map_rootOfSplits'
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem natDegree_eq_card_roots' {p : K[X]} {i : K →+* L} (hsplit : Splits i p) :
     (p.map i).natDegree = Multiset.card (p.map i).roots := by
   by_cases hp : p.map i = 0
@@ -229,7 +223,6 @@ theorem natDegree_eq_card_roots' {p : K[X]} {i : K →+* L} (hsplit : Splits i p
     exact mul_ne_zero monic_prod_multiset_X_sub_C.ne_zero hq
 #align polynomial.nat_degree_eq_card_roots' Polynomial.natDegree_eq_card_roots'
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem degree_eq_card_roots' {p : K[X]} {i : K →+* L} (p_ne_zero : p.map i ≠ 0)
     (hsplit : Splits i p) : (p.map i).degree = Multiset.card (p.map i).roots := by
   simp [degree_eq_natDegree p_ne_zero, natDegree_eq_card_roots' hsplit]
@@ -264,13 +257,11 @@ theorem splits_of_splits_of_dvd {f g : K[X]} (hf0 : f ≠ 0) (hf : Splits i f) (
   exact (splits_of_splits_mul i hf0 hf).1
 #align polynomial.splits_of_splits_of_dvd Polynomial.splits_of_splits_of_dvd
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem splits_of_splits_gcd_left {f g : K[X]} (hf0 : f ≠ 0) (hf : Splits i f) :
     Splits i (EuclideanDomain.gcd f g) :=
   Polynomial.splits_of_splits_of_dvd i hf0 hf (EuclideanDomain.gcd_dvd_left f g)
 #align polynomial.splits_of_splits_gcd_left Polynomial.splits_of_splits_gcd_left
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem splits_of_splits_gcd_right {f g : K[X]} (hg0 : g ≠ 0) (hg : Splits i g) :
     Splits i (EuclideanDomain.gcd f g) :=
   Polynomial.splits_of_splits_of_dvd i hg0 hg (EuclideanDomain.gcd_dvd_right f g)
@@ -332,7 +323,6 @@ theorem natDegree_eq_card_roots {p : K[X]} {i : K →+* L} (hsplit : Splits i p)
   (natDegree_map i).symm.trans <| natDegree_eq_card_roots' hsplit
 #align polynomial.nat_degree_eq_card_roots Polynomial.natDegree_eq_card_roots
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem degree_eq_card_roots {p : K[X]} {i : K →+* L} (p_ne_zero : p ≠ 0) (hsplit : Splits i p) :
     p.degree = Multiset.card (p.map i).roots := by
   rw [degree_eq_natDegree p_ne_zero, natDegree_eq_card_roots hsplit]
@@ -344,7 +334,6 @@ theorem roots_map {f : K[X]} (hf : f.Splits <| RingHom.id K) : (f.map i).roots =
       rw [map_id]).symm
 #align polynomial.roots_map Polynomial.roots_map
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem image_rootSet [Algebra F K] [Algebra F L] {p : F[X]} (h : p.Splits (algebraMap F K))
     (f : K →ₐ[F] L) : f '' p.rootSet K = p.rootSet L := by
   classical
@@ -353,7 +342,6 @@ theorem image_rootSet [Algebra F K] [Algebra F L] {p : F[X]} (h : p.Splits (alge
       ← rootSet]
 #align polynomial.image_root_set Polynomial.image_rootSet
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem adjoin_rootSet_eq_range [Algebra F K] [Algebra F L] {p : F[X]}
     (h : p.Splits (algebraMap F K)) (f : K →ₐ[F] L) :
     Algebra.adjoin F (p.rootSet L) = f.range ↔ Algebra.adjoin F (p.rootSet K) = ⊤ := by
@@ -387,7 +375,6 @@ theorem eq_X_sub_C_of_splits_of_single_root {x : K} {h : K[X]} (h_splits : Split
 set_option linter.uppercaseLean3 false in
 #align polynomial.eq_X_sub_C_of_splits_of_single_root Polynomial.eq_X_sub_C_of_splits_of_single_root
 
-set_option maxHeartbeats 400000 in -- Porting note: gets around lean4#2074
 theorem mem_lift_of_splits_of_roots_mem_range (R : Type _) [CommRing R] [Algebra R K] {f : K[X]}
     (hs : f.Splits (RingHom.id K)) (hm : f.Monic) (hr : ∀ a ∈ f.roots, a ∈ (algebraMap R K).range) :
     f ∈ Polynomial.lifts (algebraMap R K) := by
@@ -405,9 +392,6 @@ local infixl:50 " ~ᵤ " => Associated
 
 open UniqueFactorizationMonoid Associates
 
-set_option maxHeartbeats 400000 in
-set_option synthInstance.maxHeartbeats 100000 in
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem splits_of_exists_multiset {f : K[X]} {s : Multiset L}
     (hs : f.map i = C (i f.leadingCoeff) * (s.map fun a : L => X - C a).prod) : Splits i f :=
   if hf0 : f = 0 then hf0.symm ▸ splits_zero i
@@ -424,8 +408,6 @@ theorem splits_of_exists_multiset {f : K[X]} {s : Multiset L}
         exact degree_X_sub_C a
 #align polynomial.splits_of_exists_multiset Polynomial.splits_of_exists_multiset
 
-set_option synthInstance.maxHeartbeats 100000 in
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem splits_of_splits_id {f : K[X]} : Splits (RingHom.id K) f → Splits i f :=
   UniqueFactorizationMonoid.induction_on_prime f (fun _ => splits_zero _)
     (fun _ hu _ => splits_of_degree_le_one _ ((isUnit_iff_degree_eq_zero.1 hu).symm ▸ by decide))

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

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

@@ -112,7 +112,9 @@ theorem splits_of_natDegree_eq_one {f : K[X]} (hf : natDegree f = 1) : Splits i
   splits_of_natDegree_le_one i (le_of_eq hf)
 #align polynomial.splits_of_nat_degree_eq_one Polynomial.splits_of_natDegree_eq_one
 
-attribute [-instance] Ring.toNonAssocRing in -- Porting note: gets around lean4#2074
+set_option synthInstance.etaExperiment true in
+set_option synthInstance.maxHeartbeats 100000 in
+set_option maxHeartbeats 300000 in
 theorem splits_mul {f g : K[X]} (hf : Splits i f) (hg : Splits i g) : Splits i (f * g) :=
   if h : (f * g).map i = 0 then Or.inl h
   else

Co-authored-by: Matthew Ballard <matt@mrb.email>

@@ -362,7 +362,7 @@ theorem adjoin_rootSet_eq_range [Algebra F K] [Algebra F L] {p : F[X]}
 theorem eq_prod_roots_of_splits {p : K[X]} {i : K →+* L} (hsplit : Splits i p) :
     p.map i = C (i p.leadingCoeff) * ((p.map i).roots.map fun a => X - C a).prod := by
   rw [← leadingCoeff_map]; symm
-  apply c_leadingCoeff_mul_prod_multiset_X_sub_C
+  apply C_leadingCoeff_mul_prod_multiset_X_sub_C
   rw [natDegree_map]; exact (natDegree_eq_card_roots hsplit).symm
 #align polynomial.eq_prod_roots_of_splits Polynomial.eq_prod_roots_of_splits
 
@@ -462,7 +462,7 @@ theorem splits_iff_card_roots {p : K[X]} :
     rw [splits_iff_exists_multiset (RingHom.id K)]
     use p.roots
     simp only [RingHom.id_apply, map_id]
-    exact (c_leadingCoeff_mul_prod_multiset_X_sub_C hroots).symm
+    exact (C_leadingCoeff_mul_prod_multiset_X_sub_C hroots).symm
 #align polynomial.splits_iff_card_roots Polynomial.splits_iff_card_roots
 
 theorem aeval_root_derivative_of_splits [Algebra K L] {P : K[X]} (hmo : P.Monic)

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