field_theory.separable ⟷ Mathlib.FieldTheory.Separable

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: Kenny Lau
 -/
 import Algebra.Squarefree.Basic
-import Data.Polynomial.Expand
-import Data.Polynomial.Splits
+import Algebra.Polynomial.Expand
+import Algebra.Polynomial.Splits
 import FieldTheory.Minpoly.Field
 import RingTheory.PowerBasis
 

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

@@ -3,7 +3,7 @@ Copyright (c) 2020 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
 -/
-import Algebra.Squarefree
+import Algebra.Squarefree.Basic
 import Data.Polynomial.Expand
 import Data.Polynomial.Splits
 import FieldTheory.Minpoly.Field
@@ -147,7 +147,7 @@ theorem Separable.of_pow' {f : R[X]} :
   | 0 => fun h => Or.inr <| Or.inr rfl
   | 1 => fun h => Or.inr <| Or.inl ⟨pow_one f ▸ h, rfl⟩
   | n + 2 => fun h => by
-    rw [pow_succ, pow_succ] at h
+    rw [pow_succ', pow_succ'] at h
     exact Or.inl (isCoprime_self.1 h.is_coprime.of_mul_right_left)
 #align polynomial.separable.of_pow' Polynomial.Separable.of_pow'
 -/
@@ -293,7 +293,7 @@ theorem separable_X_pow_sub_C_unit {n : ℕ} (u : Rˣ) (hn : IsUnit (n : R)) :
         C (↑u⁻¹ * ↑u) - C ↑u⁻¹ * X ^ n + C ↑u⁻¹ * C (n' * ↑n) * (X * X ^ (n - 1)) :=
       by simp only [C.map_mul, C_eq_nat_cast]; ring
     _ = 1 := by
-      simp only [Units.inv_mul, hn', C.map_one, mul_one, ← pow_succ,
+      simp only [Units.inv_mul, hn', C.map_one, mul_one, ← pow_succ',
         Nat.sub_add_cancel (show 1 ≤ n from hpos), sub_add_cancel]
 #align polynomial.separable_X_pow_sub_C_unit Polynomial.separable_X_pow_sub_C_unit
 -/
@@ -417,7 +417,7 @@ theorem exists_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : p
       rw [← mul_one g.nat_degree, ← hg1]
       exact Nat.mul_lt_mul_of_pos_left hp.one_lt hg2.bot_lt
     rcases ih _ hg3 hg rfl with ⟨n, g, hg4, rfl⟩; refine' ⟨n + 1, g, hg4, _⟩
-    rw [← hgf, expand_expand, pow_succ]
+    rw [← hgf, expand_expand, pow_succ']
 #align polynomial.exists_separable_of_irreducible Polynomial.exists_separable_of_irreducible
 -/
 

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

@@ -102,14 +102,14 @@ theorem separable_C (r : R) : (C r).Separable ↔ IsUnit r := by
 #print Polynomial.Separable.of_mul_left /-
 theorem Separable.of_mul_left {f g : R[X]} (h : (f * g).Separable) : f.Separable :=
   by
-  have := h.of_mul_left_left; rw [derivative_mul] at this 
+  have := h.of_mul_left_left; rw [derivative_mul] at this
   exact IsCoprime.of_mul_right_left (IsCoprime.of_add_mul_left_right this)
 #align polynomial.separable.of_mul_left Polynomial.Separable.of_mul_left
 -/
 
 #print Polynomial.Separable.of_mul_right /-
 theorem Separable.of_mul_right {f g : R[X]} (h : (f * g).Separable) : g.Separable := by
-  rw [mul_comm] at h ; exact h.of_mul_left
+  rw [mul_comm] at h; exact h.of_mul_left
 #align polynomial.separable.of_mul_right Polynomial.Separable.of_mul_right
 -/
 
@@ -136,7 +136,7 @@ theorem separable_gcd_right {F : Type _} [Field F] {g : F[X]} (f : F[X]) (hg : g
 #print Polynomial.Separable.isCoprime /-
 theorem Separable.isCoprime {f g : R[X]} (h : (f * g).Separable) : IsCoprime f g :=
   by
-  have := h.of_mul_left_left; rw [derivative_mul] at this 
+  have := h.of_mul_left_left; rw [derivative_mul] at this
   exact IsCoprime.of_mul_right_right (IsCoprime.of_add_mul_left_right this)
 #align polynomial.separable.is_coprime Polynomial.Separable.isCoprime
 -/
@@ -147,7 +147,7 @@ theorem Separable.of_pow' {f : R[X]} :
   | 0 => fun h => Or.inr <| Or.inr rfl
   | 1 => fun h => Or.inr <| Or.inl ⟨pow_one f ▸ h, rfl⟩
   | n + 2 => fun h => by
-    rw [pow_succ, pow_succ] at h 
+    rw [pow_succ, pow_succ] at h
     exact Or.inl (isCoprime_self.1 h.is_coprime.of_mul_right_left)
 #align polynomial.separable.of_pow' Polynomial.Separable.of_pow'
 -/
@@ -233,7 +233,7 @@ theorem separable_prod' {ι : Sort _} {f : ι → R[X]} {s : Finset ι} :
       (∀ x ∈ s, (f x).Separable) → (∏ x in s, f x).Separable :=
   Finset.induction_on s (fun _ _ => separable_one) fun a s has ih h1 h2 =>
     by
-    simp_rw [Finset.forall_mem_insert, forall_and] at h1 h2 ; rw [prod_insert has]
+    simp_rw [Finset.forall_mem_insert, forall_and] at h1 h2; rw [prod_insert has]
     exact
       h2.1.mul (ih h1.2.2 h2.2)
         (IsCoprime.prod_right fun i his => h1.1.2 i his <| Ne.symm <| ne_of_mem_of_not_mem his has)
@@ -254,7 +254,7 @@ theorem Separable.inj_of_prod_X_sub_C [Nontrivial R] {ι : Sort _} {f : ι → R
   by_contra hxy
   rw [← insert_erase hx, prod_insert (not_mem_erase _ _), ←
     insert_erase (mem_erase_of_ne_of_mem (Ne.symm hxy) hy), prod_insert (not_mem_erase _ _), ←
-    mul_assoc, hfxy, ← sq] at hfs 
+    mul_assoc, hfxy, ← sq] at hfs
   cases (hfs.of_mul_left.of_pow (not_is_unit_X_sub_C _) two_ne_zero).2
 #align polynomial.separable.inj_of_prod_X_sub_C Polynomial.Separable.inj_of_prod_X_sub_C
 -/
@@ -391,7 +391,7 @@ theorem separable_or {f : F[X]} (hf : Irreducible f) :
     exact
       Or.inr
         ⟨by rw [separable_iff_derivative_ne_zero hf, Classical.not_not, H], contract p f,
-          of_irreducible_map (↑(expand F p)) (by rwa [← expand_contract p H hp.ne'] at hf ),
+          of_irreducible_map (↑(expand F p)) (by rwa [← expand_contract p H hp.ne'] at hf),
           expand_contract p H hp.ne'⟩
   else Or.inl <| (separable_iff_derivative_ne_zero hf).2 H
 #align polynomial.separable_or Polynomial.separable_or
@@ -406,13 +406,12 @@ theorem exists_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : p
   rcases separable_or p hf with (h | ⟨h1, g, hg, hgf⟩)
   · refine' ⟨0, f, h, _⟩; rw [pow_zero, expand_one]
   · cases' N with N
-    · rw [nat_degree_eq_zero_iff_degree_le_zero, degree_le_zero_iff] at hn 
-      rw [hn, separable_C, isUnit_iff_ne_zero, Classical.not_not] at h1 
+    · rw [nat_degree_eq_zero_iff_degree_le_zero, degree_le_zero_iff] at hn
+      rw [hn, separable_C, isUnit_iff_ne_zero, Classical.not_not] at h1
       have hf0 : f ≠ 0 := hf.ne_zero
-      rw [h1, C_0] at hn ; exact absurd hn hf0
+      rw [h1, C_0] at hn; exact absurd hn hf0
     have hg1 : g.nat_degree * p = N.succ := by rwa [← nat_degree_expand, hgf]
-    have hg2 : g.nat_degree ≠ 0 := by intro this; rw [this, MulZeroClass.zero_mul] at hg1 ;
-      cases hg1
+    have hg2 : g.nat_degree ≠ 0 := by intro this; rw [this, MulZeroClass.zero_mul] at hg1; cases hg1
     have hg3 : g.nat_degree < N.succ :=
       by
       rw [← mul_one g.nat_degree, ← hg1]
@@ -431,9 +430,9 @@ theorem isUnit_or_eq_zero_of_separable_expand {f : F[X]} (n : ℕ) (hp : 0 < p)
   have hf2 : (expand F (p ^ n) f).derivative = 0 := by
     rw [derivative_expand, Nat.cast_pow, CharP.cast_eq_zero, zero_pow hn.bot_lt,
       MulZeroClass.zero_mul, MulZeroClass.mul_zero]
-  rw [separable_def, hf2, isCoprime_zero_right, is_unit_iff] at hf 
+  rw [separable_def, hf2, isCoprime_zero_right, is_unit_iff] at hf
   rcases hf with ⟨r, hr, hrf⟩
-  rw [eq_comm, expand_eq_C (pow_pos hp _)] at hrf 
+  rw [eq_comm, expand_eq_C (pow_pos hp _)] at hrf
   rwa [hrf, is_unit_C]
 #align polynomial.is_unit_or_eq_zero_of_separable_expand Polynomial.isUnit_or_eq_zero_of_separable_expand
 -/
@@ -448,12 +447,12 @@ theorem unique_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : 0
   · intro g₁ g₂ hg₁ Hg₁ hg₂ Hg₂
     simpa only [eq_comm] using this hf hp n₂ n₁ (le_of_not_le hn) g₂ g₁ hg₂ Hg₂ hg₁ Hg₁
   have hf0 : f ≠ 0 := hf.ne_zero
-  intros; rw [le_iff_exists_add] at hn ; rcases hn with ⟨k, rfl⟩
-  rw [← hgf₁, pow_add, expand_mul, expand_inj (pow_pos hp n₁)] at hgf₂ ; subst hgf₂
+  intros; rw [le_iff_exists_add] at hn; rcases hn with ⟨k, rfl⟩
+  rw [← hgf₁, pow_add, expand_mul, expand_inj (pow_pos hp n₁)] at hgf₂; subst hgf₂
   subst hgf₁
   rcases is_unit_or_eq_zero_of_separable_expand p k hp hg₁ with (h | rfl)
-  · rw [is_unit_iff] at h ; rcases h with ⟨r, hr, rfl⟩
-    simp_rw [expand_C] at hf ; exact absurd (is_unit_C.2 hr) hf.1
+  · rw [is_unit_iff] at h; rcases h with ⟨r, hr, rfl⟩
+    simp_rw [expand_C] at hf; exact absurd (is_unit_C.2 hr) hf.1
   · rw [add_zero, pow_zero, expand_one]; constructor <;> rfl
 #align polynomial.unique_separable_of_irreducible Polynomial.unique_separable_of_irreducible
 -/
@@ -478,7 +477,7 @@ theorem X_pow_sub_one_separable_iff {n : ℕ} : (X ^ n - 1 : F[X]).Separable ↔
   rw [separable_def', derivative_sub, derivative_X_pow, derivative_one, sub_zero]
   -- Suppose `(n : F) = 0`, then the derivative is `0`, so `X ^ n - 1` is a unit, contradiction.
   rintro (h : IsCoprime _ _) hn'
-  rw [hn', C_0, MulZeroClass.zero_mul, isCoprime_zero_right] at h 
+  rw [hn', C_0, MulZeroClass.zero_mul, isCoprime_zero_right] at h
   exact not_is_unit_X_pow_sub_one F n h
 #align polynomial.X_pow_sub_one_separable_iff Polynomial.X_pow_sub_one_separable_iff
 -/
@@ -542,7 +541,7 @@ theorem Irreducible.separable [CharZero F] {f : F[X]} (hf : Irreducible f) : f.S
   refine' fun hf1 => hf.not_unit _
   rw [hf1, is_unit_C, isUnit_iff_ne_zero]
   intro hf2
-  rw [hf2, C_0] at hf1 
+  rw [hf2, C_0] at hf1
   exact absurd hf1 hf.ne_zero
 #align irreducible.separable Irreducible.separable
 -/
@@ -636,7 +635,7 @@ theorem isSeparable_tower_bot_of_isSeparable [h : IsSeparable F E] : IsSeparable
     obtain ⟨q, hq⟩ :=
       minpoly.dvd F x
         ((aeval_algebra_map_eq_zero_iff _ _ _).mp (minpoly.aeval F ((algebraMap K E) x)))
-    rw [hq] at hs 
+    rw [hq] at hs
     exact hs.of_mul_left
 #align is_separable_tower_bot_of_is_separable isSeparable_tower_bot_of_isSeparable
 -/

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

@@ -623,7 +623,7 @@ variable (F K E : Type _) [Field F] [Field K] [Field E] [Algebra F K] [Algebra F
 
 #print isSeparable_tower_top_of_isSeparable /-
 theorem isSeparable_tower_top_of_isSeparable [IsSeparable F E] : IsSeparable K E :=
-  ⟨fun x => isIntegral_of_isScalarTower (IsSeparable.isIntegral F x), fun x =>
+  ⟨fun x => IsIntegral.tower_top (IsSeparable.isIntegral F x), fun x =>
     (IsSeparable.separable F x).map.of_dvd (minpoly.dvd_map_of_isScalarTower _ _ _)⟩
 #align is_separable_tower_top_of_is_separable isSeparable_tower_top_of_isSeparable
 -/
@@ -632,9 +632,7 @@ theorem isSeparable_tower_top_of_isSeparable [IsSeparable F E] : IsSeparable K E
 theorem isSeparable_tower_bot_of_isSeparable [h : IsSeparable F E] : IsSeparable F K :=
   isSeparable_iff.2 fun x =>
     by
-    refine'
-      (isSeparable_iff.1 h (algebraMap K E x)).imp isIntegral_tower_bot_of_isIntegral_field
-        fun hs => _
+    refine' (isSeparable_iff.1 h (algebraMap K E x)).imp IsIntegral.tower_bot_of_field fun hs => _
     obtain ⟨q, hq⟩ :=
       minpoly.dvd F x
         ((aeval_algebra_map_eq_zero_iff _ _ _).mp (minpoly.aeval F ((algebraMap K E) x)))

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

@@ -426,7 +426,7 @@ theorem exists_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : p
 theorem isUnit_or_eq_zero_of_separable_expand {f : F[X]} (n : ℕ) (hp : 0 < p)
     (hf : (expand F (p ^ n) f).Separable) : IsUnit f ∨ n = 0 :=
   by
-  rw [or_iff_not_imp_right]
+  rw [Classical.or_iff_not_imp_right]
   rintro hn : n ≠ 0
   have hf2 : (expand F (p ^ n) f).derivative = 0 := by
     rw [derivative_expand, Nat.cast_pow, CharP.cast_eq_zero, zero_pow hn.bot_lt,

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

@@ -3,11 +3,11 @@ Copyright (c) 2020 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
 -/
-import Mathbin.Algebra.Squarefree
-import Mathbin.Data.Polynomial.Expand
-import Mathbin.Data.Polynomial.Splits
-import Mathbin.FieldTheory.Minpoly.Field
-import Mathbin.RingTheory.PowerBasis
+import Algebra.Squarefree
+import Data.Polynomial.Expand
+import Data.Polynomial.Splits
+import FieldTheory.Minpoly.Field
+import RingTheory.PowerBasis
 
 #align_import field_theory.separable from "leanprover-community/mathlib"@"61db041ab8e4aaf8cb5c7dc10a7d4ff261997536"
 

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

@@ -223,7 +223,7 @@ theorem separable_X_sub_C {x : R} : Separable (X - C x) := by
 theorem Separable.mul {f g : R[X]} (hf : f.Separable) (hg : g.Separable) (h : IsCoprime f g) :
     (f * g).Separable := by rw [separable_def, derivative_mul];
   exact
-    ((hf.mul_right h).add_mul_left_right _).mul_left ((h.symm.mul_right hg).mul_add_right_right _)
+    ((hf.mul_right h).add_mul_left_right _).hMul_left ((h.symm.mul_right hg).mul_add_right_right _)
 #align polynomial.separable.mul Polynomial.Separable.mul
 -/
 

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

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
-
-! This file was ported from Lean 3 source module field_theory.separable
-! leanprover-community/mathlib commit 61db041ab8e4aaf8cb5c7dc10a7d4ff261997536
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Squarefree
 import Mathbin.Data.Polynomial.Expand
@@ -14,6 +9,8 @@ import Mathbin.Data.Polynomial.Splits
 import Mathbin.FieldTheory.Minpoly.Field
 import Mathbin.RingTheory.PowerBasis
 
+#align_import field_theory.separable from "leanprover-community/mathlib"@"61db041ab8e4aaf8cb5c7dc10a7d4ff261997536"
+
 /-!
 
 # Separable polynomials

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

@@ -50,13 +50,17 @@ def Separable (f : R[X]) : Prop :=
 #align polynomial.separable Polynomial.Separable
 -/
 
+#print Polynomial.separable_def /-
 theorem separable_def (f : R[X]) : f.Separable ↔ IsCoprime f f.derivative :=
   Iff.rfl
 #align polynomial.separable_def Polynomial.separable_def
+-/
 
+#print Polynomial.separable_def' /-
 theorem separable_def' (f : R[X]) : f.Separable ↔ ∃ a b : R[X], a * f + b * f.derivative = 1 :=
   Iff.rfl
 #align polynomial.separable_def' Polynomial.separable_def'
+-/
 
 #print Polynomial.not_separable_zero /-
 theorem not_separable_zero [Nontrivial R] : ¬Separable (0 : R[X]) :=
@@ -78,11 +82,13 @@ theorem separable_of_subsingleton [Subsingleton R] (f : R[X]) : f.Separable := b
 #align polynomial.separable_of_subsingleton Polynomial.separable_of_subsingleton
 -/
 
+#print Polynomial.separable_X_add_C /-
 theorem separable_X_add_C (a : R) : (X + C a).Separable :=
   by
   rw [separable_def, derivative_add, derivative_X, derivative_C, add_zero]
   exact isCoprime_one_right
 #align polynomial.separable_X_add_C Polynomial.separable_X_add_C
+-/
 
 #print Polynomial.separable_X /-
 theorem separable_X : (X : R[X]).Separable := by rw [separable_def, derivative_X];
@@ -90,9 +96,11 @@ theorem separable_X : (X : R[X]).Separable := by rw [separable_def, derivative_X
 #align polynomial.separable_X Polynomial.separable_X
 -/
 
+#print Polynomial.separable_C /-
 theorem separable_C (r : R) : (C r).Separable ↔ IsUnit r := by
   rw [separable_def, derivative_C, isCoprime_zero_right, is_unit_C]
 #align polynomial.separable_C Polynomial.separable_C
+-/
 
 #print Polynomial.Separable.of_mul_left /-
 theorem Separable.of_mul_left {f g : R[X]} (h : (f * g).Separable) : f.Separable :=
@@ -114,15 +122,19 @@ theorem Separable.of_dvd {f g : R[X]} (hf : f.Separable) (hfg : g ∣ f) : g.Sep
 #align polynomial.separable.of_dvd Polynomial.Separable.of_dvd
 -/
 
+#print Polynomial.separable_gcd_left /-
 theorem separable_gcd_left {F : Type _} [Field F] {f : F[X]} (hf : f.Separable) (g : F[X]) :
     (EuclideanDomain.gcd f g).Separable :=
   Separable.of_dvd hf (EuclideanDomain.gcd_dvd_left f g)
 #align polynomial.separable_gcd_left Polynomial.separable_gcd_left
+-/
 
+#print Polynomial.separable_gcd_right /-
 theorem separable_gcd_right {F : Type _} [Field F] {g : F[X]} (f : F[X]) (hg : g.Separable) :
     (EuclideanDomain.gcd f g).Separable :=
   Separable.of_dvd hg (EuclideanDomain.gcd_dvd_right f g)
 #align polynomial.separable_gcd_right Polynomial.separable_gcd_right
+-/
 
 #print Polynomial.Separable.isCoprime /-
 theorem Separable.isCoprime {f g : R[X]} (h : (f * g).Separable) : IsCoprime f g :=
@@ -204,9 +216,11 @@ section CommRing
 
 variable {R : Type u} [CommRing R]
 
+#print Polynomial.separable_X_sub_C /-
 theorem separable_X_sub_C {x : R} : Separable (X - C x) := by
   simpa only [sub_eq_add_neg, C_neg] using separable_X_add_C (-x)
 #align polynomial.separable_X_sub_C Polynomial.separable_X_sub_C
+-/
 
 #print Polynomial.Separable.mul /-
 theorem Separable.mul {f g : R[X]} (hf : f.Separable) (hg : g.Separable) (h : IsCoprime f g) :
@@ -216,6 +230,7 @@ theorem Separable.mul {f g : R[X]} (hf : f.Separable) (hg : g.Separable) (h : Is
 #align polynomial.separable.mul Polynomial.Separable.mul
 -/
 
+#print Polynomial.separable_prod' /-
 theorem separable_prod' {ι : Sort _} {f : ι → R[X]} {s : Finset ι} :
     (∀ x ∈ s, ∀ y ∈ s, x ≠ y → IsCoprime (f x) (f y)) →
       (∀ x ∈ s, (f x).Separable) → (∏ x in s, f x).Separable :=
@@ -226,12 +241,16 @@ theorem separable_prod' {ι : Sort _} {f : ι → R[X]} {s : Finset ι} :
       h2.1.mul (ih h1.2.2 h2.2)
         (IsCoprime.prod_right fun i his => h1.1.2 i his <| Ne.symm <| ne_of_mem_of_not_mem his has)
 #align polynomial.separable_prod' Polynomial.separable_prod'
+-/
 
+#print Polynomial.separable_prod /-
 theorem separable_prod {ι : Sort _} [Fintype ι] {f : ι → R[X]} (h1 : Pairwise (IsCoprime on f))
     (h2 : ∀ x, (f x).Separable) : (∏ x, f x).Separable :=
   separable_prod' (fun x hx y hy hxy => h1 hxy) fun x hx => h2 x
 #align polynomial.separable_prod Polynomial.separable_prod
+-/
 
+#print Polynomial.Separable.inj_of_prod_X_sub_C /-
 theorem Separable.inj_of_prod_X_sub_C [Nontrivial R] {ι : Sort _} {f : ι → R} {s : Finset ι}
     (hfs : (∏ i in s, (X - C (f i))).Separable) {x y : ι} (hx : x ∈ s) (hy : y ∈ s)
     (hfxy : f x = f y) : x = y := by
@@ -241,12 +260,16 @@ theorem Separable.inj_of_prod_X_sub_C [Nontrivial R] {ι : Sort _} {f : ι → R
     mul_assoc, hfxy, ← sq] at hfs 
   cases (hfs.of_mul_left.of_pow (not_is_unit_X_sub_C _) two_ne_zero).2
 #align polynomial.separable.inj_of_prod_X_sub_C Polynomial.Separable.inj_of_prod_X_sub_C
+-/
 
+#print Polynomial.Separable.injective_of_prod_X_sub_C /-
 theorem Separable.injective_of_prod_X_sub_C [Nontrivial R] {ι : Sort _} [Fintype ι] {f : ι → R}
     (hfs : (∏ i, (X - C (f i))).Separable) : Function.Injective f := fun x y hfxy =>
   hfs.inj_of_prod_X_sub_C (mem_univ _) (mem_univ _) hfxy
 #align polynomial.separable.injective_of_prod_X_sub_C Polynomial.Separable.injective_of_prod_X_sub_C
+-/
 
+#print Polynomial.nodup_of_separable_prod /-
 theorem nodup_of_separable_prod [Nontrivial R] {s : Multiset R}
     (hs : Separable (Multiset.map (fun a => X - C a) s).Prod) : s.Nodup :=
   by
@@ -255,7 +278,9 @@ theorem nodup_of_separable_prod [Nontrivial R] {s : Multiset R}
   refine' not_is_unit_X_sub_C a (is_unit_of_self_mul_dvd_separable hs _)
   simpa only [Multiset.map_cons, Multiset.prod_cons] using mul_dvd_mul_left _ (dvd_mul_right _ _)
 #align polynomial.nodup_of_separable_prod Polynomial.nodup_of_separable_prod
+-/
 
+#print Polynomial.separable_X_pow_sub_C_unit /-
 /-- If `is_unit n` in a `comm_ring R`, then `X ^ n - u` is separable for any unit `u`. -/
 theorem separable_X_pow_sub_C_unit {n : ℕ} (u : Rˣ) (hn : IsUnit (n : R)) :
     Separable (X ^ n - C (u : R)) := by
@@ -274,6 +299,7 @@ theorem separable_X_pow_sub_C_unit {n : ℕ} (u : Rˣ) (hn : IsUnit (n : R)) :
       simp only [Units.inv_mul, hn', C.map_one, mul_one, ← pow_succ,
         Nat.sub_add_cancel (show 1 ≤ n from hpos), sub_add_cancel]
 #align polynomial.separable_X_pow_sub_C_unit Polynomial.separable_X_pow_sub_C_unit
+-/
 
 #print Polynomial.rootMultiplicity_le_one_of_separable /-
 theorem rootMultiplicity_le_one_of_separable [Nontrivial R] {p : R[X]} (hsep : Separable p)
@@ -313,6 +339,7 @@ section Field
 
 variable {F : Type u} [Field F] {K : Type v} [Field K]
 
+#print Polynomial.separable_iff_derivative_ne_zero /-
 theorem separable_iff_derivative_ne_zero {f : F[X]} (hf : Irreducible f) :
     f.Separable ↔ f.derivative ≠ 0 :=
   ⟨fun h1 h2 => hf.not_unit <| isCoprime_zero_right.1 <| h2 ▸ h1, fun h =>
@@ -322,6 +349,7 @@ theorem separable_iff_derivative_ne_zero {f : F[X]} (hf : Irreducible f) :
       not_lt_of_le (natDegree_le_of_dvd this h) <|
         natDegree_derivative_lt <| mt derivative_of_natDegree_zero h⟩
 #align polynomial.separable_iff_derivative_ne_zero Polynomial.separable_iff_derivative_ne_zero
+-/
 
 #print Polynomial.separable_map /-
 theorem separable_map (f : F →+* K) {p : F[X]} : (p.map f).Separable ↔ p.Separable := by
@@ -329,6 +357,7 @@ theorem separable_map (f : F →+* K) {p : F[X]} : (p.map f).Separable ↔ p.Sep
 #align polynomial.separable_map Polynomial.separable_map
 -/
 
+#print Polynomial.separable_prod_X_sub_C_iff' /-
 theorem separable_prod_X_sub_C_iff' {ι : Sort _} {f : ι → F} {s : Finset ι} :
     (∏ i in s, (X - C (f i))).Separable ↔ ∀ x ∈ s, ∀ y ∈ s, f x = f y → x = y :=
   ⟨fun hfs x hx y hy hfxy => hfs.inj_of_prod_X_sub_C hx hy hfxy, fun H => by rw [← prod_attach];
@@ -339,18 +368,20 @@ theorem separable_prod_X_sub_C_iff' {ι : Sort _} {f : ι → F} {s : Finset ι}
             (fun x y hxy => Subtype.eq <| H x.1 x.2 y.1 y.2 hxy) _ _ hxy)
         fun _ _ => separable_X_sub_C⟩
 #align polynomial.separable_prod_X_sub_C_iff' Polynomial.separable_prod_X_sub_C_iff'
+-/
 
+#print Polynomial.separable_prod_X_sub_C_iff /-
 theorem separable_prod_X_sub_C_iff {ι : Sort _} [Fintype ι] {f : ι → F} :
     (∏ i, (X - C (f i))).Separable ↔ Function.Injective f :=
   separable_prod_X_sub_C_iff'.trans <| by simp_rw [mem_univ, true_imp_iff, Function.Injective]
 #align polynomial.separable_prod_X_sub_C_iff Polynomial.separable_prod_X_sub_C_iff
+-/
 
 section CharP
 
 variable (p : ℕ) [HF : CharP F p]
 
-include HF
-
+#print Polynomial.separable_or /-
 theorem separable_or {f : F[X]} (hf : Irreducible f) :
     f.Separable ∨ ¬f.Separable ∧ ∃ g : F[X], Irreducible g ∧ expand F p g = f :=
   if H : f.derivative = 0 then by
@@ -367,7 +398,9 @@ theorem separable_or {f : F[X]} (hf : Irreducible f) :
           expand_contract p H hp.ne'⟩
   else Or.inl <| (separable_iff_derivative_ne_zero hf).2 H
 #align polynomial.separable_or Polynomial.separable_or
+-/
 
+#print Polynomial.exists_separable_of_irreducible /-
 theorem exists_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : p ≠ 0) :
     ∃ (n : ℕ) (g : F[X]), g.Separable ∧ expand F (p ^ n) g = f :=
   by
@@ -390,7 +423,9 @@ theorem exists_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : p
     rcases ih _ hg3 hg rfl with ⟨n, g, hg4, rfl⟩; refine' ⟨n + 1, g, hg4, _⟩
     rw [← hgf, expand_expand, pow_succ]
 #align polynomial.exists_separable_of_irreducible Polynomial.exists_separable_of_irreducible
+-/
 
+#print Polynomial.isUnit_or_eq_zero_of_separable_expand /-
 theorem isUnit_or_eq_zero_of_separable_expand {f : F[X]} (n : ℕ) (hp : 0 < p)
     (hf : (expand F (p ^ n) f).Separable) : IsUnit f ∨ n = 0 :=
   by
@@ -404,7 +439,9 @@ theorem isUnit_or_eq_zero_of_separable_expand {f : F[X]} (n : ℕ) (hp : 0 < p)
   rw [eq_comm, expand_eq_C (pow_pos hp _)] at hrf 
   rwa [hrf, is_unit_C]
 #align polynomial.is_unit_or_eq_zero_of_separable_expand Polynomial.isUnit_or_eq_zero_of_separable_expand
+-/
 
+#print Polynomial.unique_separable_of_irreducible /-
 theorem unique_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : 0 < p) (n₁ : ℕ)
     (g₁ : F[X]) (hg₁ : g₁.Separable) (hgf₁ : expand F (p ^ n₁) g₁ = f) (n₂ : ℕ) (g₂ : F[X])
     (hg₂ : g₂.Separable) (hgf₂ : expand F (p ^ n₂) g₂ = f) : n₁ = n₂ ∧ g₁ = g₂ :=
@@ -422,15 +459,19 @@ theorem unique_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : 0
     simp_rw [expand_C] at hf ; exact absurd (is_unit_C.2 hr) hf.1
   · rw [add_zero, pow_zero, expand_one]; constructor <;> rfl
 #align polynomial.unique_separable_of_irreducible Polynomial.unique_separable_of_irreducible
+-/
 
 end CharP
 
+#print Polynomial.separable_X_pow_sub_C /-
 /-- If `n ≠ 0` in `F`, then ` X ^ n - a` is separable for any `a ≠ 0`. -/
 theorem separable_X_pow_sub_C {n : ℕ} (a : F) (hn : (n : F) ≠ 0) (ha : a ≠ 0) :
     Separable (X ^ n - C a) :=
   separable_X_pow_sub_C_unit (Units.mk0 a ha) (IsUnit.mk0 n hn)
 #align polynomial.separable_X_pow_sub_C Polynomial.separable_X_pow_sub_C
+-/
 
+#print Polynomial.X_pow_sub_one_separable_iff /-
 -- this can possibly be strengthened to making `separable_X_pow_sub_C_unit` a
 -- bi-implication, but it is nontrivial!
 /-- In a field `F`, `X ^ n - 1` is separable iff `↑n ≠ 0`. -/
@@ -443,6 +484,7 @@ theorem X_pow_sub_one_separable_iff {n : ℕ} : (X ^ n - 1 : F[X]).Separable ↔
   rw [hn', C_0, MulZeroClass.zero_mul, isCoprime_zero_right] at h 
   exact not_is_unit_X_pow_sub_one F n h
 #align polynomial.X_pow_sub_one_separable_iff Polynomial.X_pow_sub_one_separable_iff
+-/
 
 section Splits
 
@@ -458,6 +500,7 @@ theorem card_rootSet_eq_natDegree [Algebra F K] {p : F[X]} (hsep : p.Separable)
 
 variable {i : F →+* K}
 
+#print Polynomial.eq_X_sub_C_of_separable_of_root_eq /-
 theorem eq_X_sub_C_of_separable_of_root_eq {x : F} {h : F[X]} (h_sep : h.Separable)
     (h_root : h.eval x = 0) (h_splits : Splits i h) (h_roots : ∀ y ∈ (h.map i).roots, y = i x) :
     h = C (leadingCoeff h) * (X - C x) :=
@@ -475,7 +518,9 @@ theorem eq_X_sub_C_of_separable_of_root_eq {x : F} {h : F[X]} (h_sep : h.Separab
     · exact h_roots
   · exact nodup_roots (separable.map h_sep)
 #align polynomial.eq_X_sub_C_of_separable_of_root_eq Polynomial.eq_X_sub_C_of_separable_of_root_eq
+-/
 
+#print Polynomial.exists_finset_of_splits /-
 theorem exists_finset_of_splits (i : F →+* K) {f : F[X]} (sep : Separable f) (sp : Splits i f) :
     ∃ s : Finset K, f.map i = C (i f.leadingCoeff) * s.Prod fun a : K => X - C a :=
   by
@@ -487,9 +532,11 @@ theorem exists_finset_of_splits (i : F →+* K) {f : F[X]} (sep : Separable f) (
   rw [← h]
   exact sep.map
 #align polynomial.exists_finset_of_splits Polynomial.exists_finset_of_splits
+-/
 
 end Splits
 
+#print Irreducible.separable /-
 theorem Irreducible.separable [CharZero F] {f : F[X]} (hf : Irreducible f) : f.Separable :=
   by
   rw [separable_iff_derivative_ne_zero hf, Ne, ← degree_eq_bot, degree_derivative_eq]
@@ -501,6 +548,7 @@ theorem Irreducible.separable [CharZero F] {f : F[X]} (hf : Irreducible f) : f.S
   rw [hf2, C_0] at hf1 
   exact absurd hf1 hf.ne_zero
 #align irreducible.separable Irreducible.separable
+-/
 
 end Field
 
@@ -532,20 +580,26 @@ class IsSeparable : Prop where
 
 variable (F) {K}
 
+#print IsSeparable.isIntegral /-
 theorem IsSeparable.isIntegral [IsSeparable F K] : ∀ x : K, IsIntegral F x :=
   IsSeparable.is_integral'
 #align is_separable.is_integral IsSeparable.isIntegral
+-/
 
+#print IsSeparable.separable /-
 theorem IsSeparable.separable [IsSeparable F K] : ∀ x : K, (minpoly F x).Separable :=
   IsSeparable.separable'
 #align is_separable.separable IsSeparable.separable
+-/
 
 variable {F K}
 
+#print isSeparable_iff /-
 theorem isSeparable_iff : IsSeparable F K ↔ ∀ x : K, IsIntegral F x ∧ (minpoly F x).Separable :=
   ⟨fun h x => ⟨@IsSeparable.isIntegral F _ _ _ h x, @IsSeparable.separable F _ _ _ h x⟩, fun h =>
     ⟨fun x => (h x).1, fun x => (h x).2⟩⟩
 #align is_separable_iff isSeparable_iff
+-/
 
 end CommRing
 
@@ -555,6 +609,7 @@ instance isSeparable_self (F : Type _) [Field F] : IsSeparable F F :=
 #align is_separable_self isSeparable_self
 -/
 
+#print IsSeparable.of_finite /-
 -- See note [lower instance priority]
 /-- A finite field extension in characteristic 0 is separable. -/
 instance (priority := 100) IsSeparable.of_finite (F K : Type _) [Field F] [Field K] [Algebra F K]
@@ -562,17 +617,21 @@ instance (priority := 100) IsSeparable.of_finite (F K : Type _) [Field F] [Field
   have : ∀ x : K, IsIntegral F x := fun x => Algebra.isIntegral_of_finite _ _ _
   ⟨this, fun x => (minpoly.irreducible (this x)).Separable⟩
 #align is_separable.of_finite IsSeparable.of_finite
+-/
 
 section IsSeparableTower
 
 variable (F K E : Type _) [Field F] [Field K] [Field E] [Algebra F K] [Algebra F E] [Algebra K E]
   [IsScalarTower F K E]
 
+#print isSeparable_tower_top_of_isSeparable /-
 theorem isSeparable_tower_top_of_isSeparable [IsSeparable F E] : IsSeparable K E :=
   ⟨fun x => isIntegral_of_isScalarTower (IsSeparable.isIntegral F x), fun x =>
     (IsSeparable.separable F x).map.of_dvd (minpoly.dvd_map_of_isScalarTower _ _ _)⟩
 #align is_separable_tower_top_of_is_separable isSeparable_tower_top_of_isSeparable
+-/
 
+#print isSeparable_tower_bot_of_isSeparable /-
 theorem isSeparable_tower_bot_of_isSeparable [h : IsSeparable F E] : IsSeparable F K :=
   isSeparable_iff.2 fun x =>
     by
@@ -585,9 +644,11 @@ theorem isSeparable_tower_bot_of_isSeparable [h : IsSeparable F E] : IsSeparable
     rw [hq] at hs 
     exact hs.of_mul_left
 #align is_separable_tower_bot_of_is_separable isSeparable_tower_bot_of_isSeparable
+-/
 
 variable {E}
 
+#print IsSeparable.of_algHom /-
 theorem IsSeparable.of_algHom (E' : Type _) [Field E'] [Algebra F E'] (f : E →ₐ[F] E')
     [IsSeparable F E'] : IsSeparable F E :=
   by
@@ -595,6 +656,7 @@ theorem IsSeparable.of_algHom (E' : Type _) [Field E'] [Algebra F E'] (f : E →
   haveI : IsScalarTower F E E' := IsScalarTower.of_algebraMap_eq fun x => (f.commutes x).symm
   exact isSeparable_tower_bot_of_isSeparable F E E'
 #align is_separable.of_alg_hom IsSeparable.of_algHom
+-/
 
 end IsSeparableTower
 
@@ -606,6 +668,7 @@ variable {K L F : Type _} [Field K] [Field L] [Field F]
 
 variable [Algebra K S] [Algebra K L]
 
+#print AlgHom.card_of_powerBasis /-
 theorem AlgHom.card_of_powerBasis (pb : PowerBasis K S) (h_sep : (minpoly K pb.gen).Separable)
     (h_splits : (minpoly K pb.gen).Splits (algebraMap K L)) :
     @Fintype.card (S →ₐ[K] L) (PowerBasis.AlgHom.fintype pb) = pb.dim :=
@@ -616,6 +679,7 @@ theorem AlgHom.card_of_powerBasis (pb : PowerBasis K S) (h_sep : (minpoly K pb.g
     nat_degree_eq_card_roots h_splits, Multiset.toFinset_card_of_nodup]
   exact nodup_roots ((separable_map (algebraMap K L)).mpr h_sep)
 #align alg_hom.card_of_power_basis AlgHom.card_of_powerBasis
+-/
 
 end CardAlgHom
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

@@ -233,7 +233,7 @@ theorem separable_prod {ι : Sort _} [Fintype ι] {f : ι → R[X]} (h1 : Pairwi
 #align polynomial.separable_prod Polynomial.separable_prod
 
 theorem Separable.inj_of_prod_X_sub_C [Nontrivial R] {ι : Sort _} {f : ι → R} {s : Finset ι}
-    (hfs : (∏ i in s, X - C (f i)).Separable) {x y : ι} (hx : x ∈ s) (hy : y ∈ s)
+    (hfs : (∏ i in s, (X - C (f i))).Separable) {x y : ι} (hx : x ∈ s) (hy : y ∈ s)
     (hfxy : f x = f y) : x = y := by
   by_contra hxy
   rw [← insert_erase hx, prod_insert (not_mem_erase _ _), ←
@@ -243,7 +243,7 @@ theorem Separable.inj_of_prod_X_sub_C [Nontrivial R] {ι : Sort _} {f : ι → R
 #align polynomial.separable.inj_of_prod_X_sub_C Polynomial.Separable.inj_of_prod_X_sub_C
 
 theorem Separable.injective_of_prod_X_sub_C [Nontrivial R] {ι : Sort _} [Fintype ι] {f : ι → R}
-    (hfs : (∏ i, X - C (f i)).Separable) : Function.Injective f := fun x y hfxy =>
+    (hfs : (∏ i, (X - C (f i))).Separable) : Function.Injective f := fun x y hfxy =>
   hfs.inj_of_prod_X_sub_C (mem_univ _) (mem_univ _) hfxy
 #align polynomial.separable.injective_of_prod_X_sub_C Polynomial.Separable.injective_of_prod_X_sub_C
 
@@ -330,7 +330,7 @@ theorem separable_map (f : F →+* K) {p : F[X]} : (p.map f).Separable ↔ p.Sep
 -/
 
 theorem separable_prod_X_sub_C_iff' {ι : Sort _} {f : ι → F} {s : Finset ι} :
-    (∏ i in s, X - C (f i)).Separable ↔ ∀ x ∈ s, ∀ y ∈ s, f x = f y → x = y :=
+    (∏ i in s, (X - C (f i))).Separable ↔ ∀ x ∈ s, ∀ y ∈ s, f x = f y → x = y :=
   ⟨fun hfs x hx y hy hfxy => hfs.inj_of_prod_X_sub_C hx hy hfxy, fun H => by rw [← prod_attach];
     exact
       separable_prod'
@@ -341,7 +341,7 @@ theorem separable_prod_X_sub_C_iff' {ι : Sort _} {f : ι → F} {s : Finset ι}
 #align polynomial.separable_prod_X_sub_C_iff' Polynomial.separable_prod_X_sub_C_iff'
 
 theorem separable_prod_X_sub_C_iff {ι : Sort _} [Fintype ι] {f : ι → F} :
-    (∏ i, X - C (f i)).Separable ↔ Function.Injective f :=
+    (∏ i, (X - C (f i))).Separable ↔ Function.Injective f :=
   separable_prod_X_sub_C_iff'.trans <| by simp_rw [mem_univ, true_imp_iff, Function.Injective]
 #align polynomial.separable_prod_X_sub_C_iff Polynomial.separable_prod_X_sub_C_iff
 

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

@@ -273,7 +273,6 @@ theorem separable_X_pow_sub_C_unit {n : ℕ} (u : Rˣ) (hn : IsUnit (n : R)) :
     _ = 1 := by
       simp only [Units.inv_mul, hn', C.map_one, mul_one, ← pow_succ,
         Nat.sub_add_cancel (show 1 ≤ n from hpos), sub_add_cancel]
-    
 #align polynomial.separable_X_pow_sub_C_unit Polynomial.separable_X_pow_sub_C_unit
 
 #print Polynomial.rootMultiplicity_le_one_of_separable /-

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

@@ -97,14 +97,14 @@ theorem separable_C (r : R) : (C r).Separable ↔ IsUnit r := by
 #print Polynomial.Separable.of_mul_left /-
 theorem Separable.of_mul_left {f g : R[X]} (h : (f * g).Separable) : f.Separable :=
   by
-  have := h.of_mul_left_left; rw [derivative_mul] at this
+  have := h.of_mul_left_left; rw [derivative_mul] at this 
   exact IsCoprime.of_mul_right_left (IsCoprime.of_add_mul_left_right this)
 #align polynomial.separable.of_mul_left Polynomial.Separable.of_mul_left
 -/
 
 #print Polynomial.Separable.of_mul_right /-
 theorem Separable.of_mul_right {f g : R[X]} (h : (f * g).Separable) : g.Separable := by
-  rw [mul_comm] at h; exact h.of_mul_left
+  rw [mul_comm] at h ; exact h.of_mul_left
 #align polynomial.separable.of_mul_right Polynomial.Separable.of_mul_right
 -/
 
@@ -127,7 +127,7 @@ theorem separable_gcd_right {F : Type _} [Field F] {g : F[X]} (f : F[X]) (hg : g
 #print Polynomial.Separable.isCoprime /-
 theorem Separable.isCoprime {f g : R[X]} (h : (f * g).Separable) : IsCoprime f g :=
   by
-  have := h.of_mul_left_left; rw [derivative_mul] at this
+  have := h.of_mul_left_left; rw [derivative_mul] at this 
   exact IsCoprime.of_mul_right_right (IsCoprime.of_add_mul_left_right this)
 #align polynomial.separable.is_coprime Polynomial.Separable.isCoprime
 -/
@@ -138,7 +138,7 @@ theorem Separable.of_pow' {f : R[X]} :
   | 0 => fun h => Or.inr <| Or.inr rfl
   | 1 => fun h => Or.inr <| Or.inl ⟨pow_one f ▸ h, rfl⟩
   | n + 2 => fun h => by
-    rw [pow_succ, pow_succ] at h
+    rw [pow_succ, pow_succ] at h 
     exact Or.inl (isCoprime_self.1 h.is_coprime.of_mul_right_left)
 #align polynomial.separable.of_pow' Polynomial.Separable.of_pow'
 -/
@@ -221,7 +221,7 @@ theorem separable_prod' {ι : Sort _} {f : ι → R[X]} {s : Finset ι} :
       (∀ x ∈ s, (f x).Separable) → (∏ x in s, f x).Separable :=
   Finset.induction_on s (fun _ _ => separable_one) fun a s has ih h1 h2 =>
     by
-    simp_rw [Finset.forall_mem_insert, forall_and] at h1 h2; rw [prod_insert has]
+    simp_rw [Finset.forall_mem_insert, forall_and] at h1 h2 ; rw [prod_insert has]
     exact
       h2.1.mul (ih h1.2.2 h2.2)
         (IsCoprime.prod_right fun i his => h1.1.2 i his <| Ne.symm <| ne_of_mem_of_not_mem his has)
@@ -238,7 +238,7 @@ theorem Separable.inj_of_prod_X_sub_C [Nontrivial R] {ι : Sort _} {f : ι → R
   by_contra hxy
   rw [← insert_erase hx, prod_insert (not_mem_erase _ _), ←
     insert_erase (mem_erase_of_ne_of_mem (Ne.symm hxy) hy), prod_insert (not_mem_erase _ _), ←
-    mul_assoc, hfxy, ← sq] at hfs
+    mul_assoc, hfxy, ← sq] at hfs 
   cases (hfs.of_mul_left.of_pow (not_is_unit_X_sub_C _) two_ne_zero).2
 #align polynomial.separable.inj_of_prod_X_sub_C Polynomial.Separable.inj_of_prod_X_sub_C
 
@@ -364,25 +364,26 @@ theorem separable_or {f : F[X]} (hf : Irreducible f) :
     exact
       Or.inr
         ⟨by rw [separable_iff_derivative_ne_zero hf, Classical.not_not, H], contract p f,
-          of_irreducible_map (↑(expand F p)) (by rwa [← expand_contract p H hp.ne'] at hf),
+          of_irreducible_map (↑(expand F p)) (by rwa [← expand_contract p H hp.ne'] at hf ),
           expand_contract p H hp.ne'⟩
   else Or.inl <| (separable_iff_derivative_ne_zero hf).2 H
 #align polynomial.separable_or Polynomial.separable_or
 
 theorem exists_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : p ≠ 0) :
-    ∃ (n : ℕ)(g : F[X]), g.Separable ∧ expand F (p ^ n) g = f :=
+    ∃ (n : ℕ) (g : F[X]), g.Separable ∧ expand F (p ^ n) g = f :=
   by
   replace hp : p.prime := (CharP.char_is_prime_or_zero F p).resolve_right hp
   induction' hn : f.nat_degree using Nat.strong_induction_on with N ih generalizing f
   rcases separable_or p hf with (h | ⟨h1, g, hg, hgf⟩)
   · refine' ⟨0, f, h, _⟩; rw [pow_zero, expand_one]
   · cases' N with N
-    · rw [nat_degree_eq_zero_iff_degree_le_zero, degree_le_zero_iff] at hn
-      rw [hn, separable_C, isUnit_iff_ne_zero, Classical.not_not] at h1
+    · rw [nat_degree_eq_zero_iff_degree_le_zero, degree_le_zero_iff] at hn 
+      rw [hn, separable_C, isUnit_iff_ne_zero, Classical.not_not] at h1 
       have hf0 : f ≠ 0 := hf.ne_zero
-      rw [h1, C_0] at hn; exact absurd hn hf0
+      rw [h1, C_0] at hn ; exact absurd hn hf0
     have hg1 : g.nat_degree * p = N.succ := by rwa [← nat_degree_expand, hgf]
-    have hg2 : g.nat_degree ≠ 0 := by intro this; rw [this, MulZeroClass.zero_mul] at hg1; cases hg1
+    have hg2 : g.nat_degree ≠ 0 := by intro this; rw [this, MulZeroClass.zero_mul] at hg1 ;
+      cases hg1
     have hg3 : g.nat_degree < N.succ :=
       by
       rw [← mul_one g.nat_degree, ← hg1]
@@ -399,9 +400,9 @@ theorem isUnit_or_eq_zero_of_separable_expand {f : F[X]} (n : ℕ) (hp : 0 < p)
   have hf2 : (expand F (p ^ n) f).derivative = 0 := by
     rw [derivative_expand, Nat.cast_pow, CharP.cast_eq_zero, zero_pow hn.bot_lt,
       MulZeroClass.zero_mul, MulZeroClass.mul_zero]
-  rw [separable_def, hf2, isCoprime_zero_right, is_unit_iff] at hf
+  rw [separable_def, hf2, isCoprime_zero_right, is_unit_iff] at hf 
   rcases hf with ⟨r, hr, hrf⟩
-  rw [eq_comm, expand_eq_C (pow_pos hp _)] at hrf
+  rw [eq_comm, expand_eq_C (pow_pos hp _)] at hrf 
   rwa [hrf, is_unit_C]
 #align polynomial.is_unit_or_eq_zero_of_separable_expand Polynomial.isUnit_or_eq_zero_of_separable_expand
 
@@ -414,12 +415,12 @@ theorem unique_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : 0
   · intro g₁ g₂ hg₁ Hg₁ hg₂ Hg₂
     simpa only [eq_comm] using this hf hp n₂ n₁ (le_of_not_le hn) g₂ g₁ hg₂ Hg₂ hg₁ Hg₁
   have hf0 : f ≠ 0 := hf.ne_zero
-  intros ; rw [le_iff_exists_add] at hn; rcases hn with ⟨k, rfl⟩
-  rw [← hgf₁, pow_add, expand_mul, expand_inj (pow_pos hp n₁)] at hgf₂; subst hgf₂
+  intros; rw [le_iff_exists_add] at hn ; rcases hn with ⟨k, rfl⟩
+  rw [← hgf₁, pow_add, expand_mul, expand_inj (pow_pos hp n₁)] at hgf₂ ; subst hgf₂
   subst hgf₁
   rcases is_unit_or_eq_zero_of_separable_expand p k hp hg₁ with (h | rfl)
-  · rw [is_unit_iff] at h; rcases h with ⟨r, hr, rfl⟩
-    simp_rw [expand_C] at hf; exact absurd (is_unit_C.2 hr) hf.1
+  · rw [is_unit_iff] at h ; rcases h with ⟨r, hr, rfl⟩
+    simp_rw [expand_C] at hf ; exact absurd (is_unit_C.2 hr) hf.1
   · rw [add_zero, pow_zero, expand_one]; constructor <;> rfl
 #align polynomial.unique_separable_of_irreducible Polynomial.unique_separable_of_irreducible
 
@@ -440,7 +441,7 @@ theorem X_pow_sub_one_separable_iff {n : ℕ} : (X ^ n - 1 : F[X]).Separable ↔
   rw [separable_def', derivative_sub, derivative_X_pow, derivative_one, sub_zero]
   -- Suppose `(n : F) = 0`, then the derivative is `0`, so `X ^ n - 1` is a unit, contradiction.
   rintro (h : IsCoprime _ _) hn'
-  rw [hn', C_0, MulZeroClass.zero_mul, isCoprime_zero_right] at h
+  rw [hn', C_0, MulZeroClass.zero_mul, isCoprime_zero_right] at h 
   exact not_is_unit_X_pow_sub_one F n h
 #align polynomial.X_pow_sub_one_separable_iff Polynomial.X_pow_sub_one_separable_iff
 
@@ -498,7 +499,7 @@ theorem Irreducible.separable [CharZero F] {f : F[X]} (hf : Irreducible f) : f.S
   refine' fun hf1 => hf.not_unit _
   rw [hf1, is_unit_C, isUnit_iff_ne_zero]
   intro hf2
-  rw [hf2, C_0] at hf1
+  rw [hf2, C_0] at hf1 
   exact absurd hf1 hf.ne_zero
 #align irreducible.separable Irreducible.separable
 
@@ -582,7 +583,7 @@ theorem isSeparable_tower_bot_of_isSeparable [h : IsSeparable F E] : IsSeparable
     obtain ⟨q, hq⟩ :=
       minpoly.dvd F x
         ((aeval_algebra_map_eq_zero_iff _ _ _).mp (minpoly.aeval F ((algebraMap K E) x)))
-    rw [hq] at hs
+    rw [hq] at hs 
     exact hs.of_mul_left
 #align is_separable_tower_bot_of_is_separable isSeparable_tower_bot_of_isSeparable
 

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

@@ -33,7 +33,7 @@ properties about separable polynomials here.
 
 universe u v w
 
-open Classical BigOperators Polynomial
+open scoped Classical BigOperators Polynomial
 
 open Finset
 

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

@@ -50,19 +50,10 @@ def Separable (f : R[X]) : Prop :=
 #align polynomial.separable Polynomial.Separable
 -/
 
-/- warning: polynomial.separable_def -> Polynomial.separable_def is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Iff (Polynomial.Separable.{u1} R _inst_1 f) (IsCoprime.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1) f (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) f))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Iff (Polynomial.Separable.{u1} R _inst_1 f) (IsCoprime.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1) f (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) f))
-Case conversion may be inaccurate. Consider using '#align polynomial.separable_def Polynomial.separable_defₓ'. -/
 theorem separable_def (f : R[X]) : f.Separable ↔ IsCoprime f f.derivative :=
   Iff.rfl
 #align polynomial.separable_def Polynomial.separable_def
 
-/- warning: polynomial.separable_def' -> Polynomial.separable_def' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.separable_def' Polynomial.separable_def'ₓ'. -/
 theorem separable_def' (f : R[X]) : f.Separable ↔ ∃ a b : R[X], a * f + b * f.derivative = 1 :=
   Iff.rfl
 #align polynomial.separable_def' Polynomial.separable_def'
@@ -87,12 +78,6 @@ theorem separable_of_subsingleton [Subsingleton R] (f : R[X]) : f.Separable := b
 #align polynomial.separable_of_subsingleton Polynomial.separable_of_subsingleton
 -/
 
-/- warning: polynomial.separable_X_add_C -> Polynomial.separable_X_add_C is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (a : R), Polynomial.Separable.{u1} R _inst_1 (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (a : R), Polynomial.Separable.{u1} R _inst_1 (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a))
-Case conversion may be inaccurate. Consider using '#align polynomial.separable_X_add_C Polynomial.separable_X_add_Cₓ'. -/
 theorem separable_X_add_C (a : R) : (X + C a).Separable :=
   by
   rw [separable_def, derivative_add, derivative_X, derivative_C, add_zero]
@@ -105,12 +90,6 @@ theorem separable_X : (X : R[X]).Separable := by rw [separable_def, derivative_X
 #align polynomial.separable_X Polynomial.separable_X
 -/
 
-/- warning: polynomial.separable_C -> Polynomial.separable_C is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (r : R), Iff (Polynomial.Separable.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) r)) (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) r)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (r : R), Iff (Polynomial.Separable.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) r)) (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) r)
-Case conversion may be inaccurate. Consider using '#align polynomial.separable_C Polynomial.separable_Cₓ'. -/
 theorem separable_C (r : R) : (C r).Separable ↔ IsUnit r := by
   rw [separable_def, derivative_C, isCoprime_zero_right, is_unit_C]
 #align polynomial.separable_C Polynomial.separable_C
@@ -135,23 +114,11 @@ theorem Separable.of_dvd {f g : R[X]} (hf : f.Separable) (hfg : g ∣ f) : g.Sep
 #align polynomial.separable.of_dvd Polynomial.Separable.of_dvd
 -/
 
-/- warning: polynomial.separable_gcd_left -> Polynomial.separable_gcd_left is a dubious translation:
-lean 3 declaration is
-  forall {F : Type.{u1}} [_inst_3 : Field.{u1} F] {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_3)))}, (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) f) -> (forall (g : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_3)))), Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (EuclideanDomain.gcd.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_3)))) (Polynomial.euclideanDomain.{u1} F _inst_3) (fun (a : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_3)))) (b : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_3)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_3)))) a b)) f g))
-but is expected to have type
-  forall {F : Type.{u1}} [_inst_3 : Field.{u1} F] {f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)))}, (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) f) -> (forall (g : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)))), Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (EuclideanDomain.gcd.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_3) (fun (a : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)))) (b : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)))) a b)) f g))
-Case conversion may be inaccurate. Consider using '#align polynomial.separable_gcd_left Polynomial.separable_gcd_leftₓ'. -/
 theorem separable_gcd_left {F : Type _} [Field F] {f : F[X]} (hf : f.Separable) (g : F[X]) :
     (EuclideanDomain.gcd f g).Separable :=
   Separable.of_dvd hf (EuclideanDomain.gcd_dvd_left f g)
 #align polynomial.separable_gcd_left Polynomial.separable_gcd_left
 
-/- warning: polynomial.separable_gcd_right -> Polynomial.separable_gcd_right is a dubious translation:
-lean 3 declaration is
-  forall {F : Type.{u1}} [_inst_3 : Field.{u1} F] {g : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_3)))} (f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_3)))), (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) g) -> (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (EuclideanDomain.gcd.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_3)))) (Polynomial.euclideanDomain.{u1} F _inst_3) (fun (a : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_3)))) (b : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_3)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_3)))) a b)) f g))
-but is expected to have type
-  forall {F : Type.{u1}} [_inst_3 : Field.{u1} F] {g : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)))} (f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)))), (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) g) -> (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (EuclideanDomain.gcd.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_3) (fun (a : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)))) (b : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)))) a b)) f g))
-Case conversion may be inaccurate. Consider using '#align polynomial.separable_gcd_right Polynomial.separable_gcd_rightₓ'. -/
 theorem separable_gcd_right {F : Type _} [Field F] {g : F[X]} (f : F[X]) (hg : g.Separable) :
     (EuclideanDomain.gcd f g).Separable :=
   Separable.of_dvd hg (EuclideanDomain.gcd_dvd_right f g)
@@ -237,12 +204,6 @@ section CommRing
 
 variable {R : Type u} [CommRing R]
 
-/- warning: polynomial.separable_X_sub_C -> Polynomial.separable_X_sub_C is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R}, Polynomial.Separable.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) x))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R}, Polynomial.Separable.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) x) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) x))
-Case conversion may be inaccurate. Consider using '#align polynomial.separable_X_sub_C Polynomial.separable_X_sub_Cₓ'. -/
 theorem separable_X_sub_C {x : R} : Separable (X - C x) := by
   simpa only [sub_eq_add_neg, C_neg] using separable_X_add_C (-x)
 #align polynomial.separable_X_sub_C Polynomial.separable_X_sub_C
@@ -255,12 +216,6 @@ theorem Separable.mul {f g : R[X]} (hf : f.Separable) (hg : g.Separable) (h : Is
 #align polynomial.separable.mul Polynomial.Separable.mul
 -/
 
-/- warning: polynomial.separable_prod' -> Polynomial.separable_prod' is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {ι : Type.{u2}} {f : ι -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))} {s : Finset.{u2} ι}, (forall (x : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) x s) -> (forall (y : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) y s) -> (Ne.{succ u2} ι x y) -> (IsCoprime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (f x) (f y)))) -> (forall (x : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) x s) -> (Polynomial.Separable.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (f x))) -> (Polynomial.Separable.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Finset.prod.{u1, u2} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) s (fun (x : ι) => f x)))
-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {ι : Type.{u1}} {f : ι -> (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))} {s : Finset.{u1} ι}, (forall (x : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) x s) -> (forall (y : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) y s) -> (Ne.{succ u1} ι x y) -> (IsCoprime.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.commSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (f x) (f y)))) -> (forall (x : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) x s) -> (Polynomial.Separable.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1) (f x))) -> (Polynomial.Separable.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1) (Finset.prod.{u2, u1} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.commRing.{u2} R _inst_1)) s (fun (x : ι) => f x)))
-Case conversion may be inaccurate. Consider using '#align polynomial.separable_prod' Polynomial.separable_prod'ₓ'. -/
 theorem separable_prod' {ι : Sort _} {f : ι → R[X]} {s : Finset ι} :
     (∀ x ∈ s, ∀ y ∈ s, x ≠ y → IsCoprime (f x) (f y)) →
       (∀ x ∈ s, (f x).Separable) → (∏ x in s, f x).Separable :=
@@ -272,23 +227,11 @@ theorem separable_prod' {ι : Sort _} {f : ι → R[X]} {s : Finset ι} :
         (IsCoprime.prod_right fun i his => h1.1.2 i his <| Ne.symm <| ne_of_mem_of_not_mem his has)
 #align polynomial.separable_prod' Polynomial.separable_prod'
 
-/- warning: polynomial.separable_prod -> Polynomial.separable_prod is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {ι : Type.{u2}} [_inst_2 : Fintype.{u2} ι] {f : ι -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))}, (Pairwise.{u2} ι (Function.onFun.{succ u2, succ u1, 1} ι (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Prop (IsCoprime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) f)) -> (forall (x : ι), Polynomial.Separable.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (f x)) -> (Polynomial.Separable.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Finset.prod.{u1, u2} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Finset.univ.{u2} ι _inst_2) (fun (x : ι) => f x)))
-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {ι : Type.{u1}} [_inst_2 : Fintype.{u1} ι] {f : ι -> (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))}, (Pairwise.{u1} ι (Function.onFun.{succ u1, succ u2, 1} ι (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Prop (IsCoprime.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.commSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) f)) -> (forall (x : ι), Polynomial.Separable.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1) (f x)) -> (Polynomial.Separable.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1) (Finset.prod.{u2, u1} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.commRing.{u2} R _inst_1)) (Finset.univ.{u1} ι _inst_2) (fun (x : ι) => f x)))
-Case conversion may be inaccurate. Consider using '#align polynomial.separable_prod Polynomial.separable_prodₓ'. -/
 theorem separable_prod {ι : Sort _} [Fintype ι] {f : ι → R[X]} (h1 : Pairwise (IsCoprime on f))
     (h2 : ∀ x, (f x).Separable) : (∏ x, f x).Separable :=
   separable_prod' (fun x hx y hy hxy => h1 hxy) fun x hx => h2 x
 #align polynomial.separable_prod Polynomial.separable_prod
 
-/- warning: polynomial.separable.inj_of_prod_X_sub_C -> Polynomial.Separable.inj_of_prod_X_sub_C is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] {ι : Type.{u2}} {f : ι -> R} {s : Finset.{u2} ι}, (Polynomial.Separable.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Finset.prod.{u1, u2} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) s (fun (i : ι) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (f i))))) -> (forall {x : ι} {y : ι}, (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) x s) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) y s) -> (Eq.{succ u1} R (f x) (f y)) -> (Eq.{succ u2} ι x y))
-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] [_inst_2 : Nontrivial.{u2} R] {ι : Type.{u1}} {f : ι -> R} {s : Finset.{u1} ι}, (Polynomial.Separable.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1) (Finset.prod.{u2, u1} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.commRing.{u2} R _inst_1)) s (fun (i : ι) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (f i)) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (instHSub.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.sub.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Polynomial.X.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Polynomial.C.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (f i))))) -> (forall {x : ι} {y : ι}, (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) x s) -> (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) y s) -> (Eq.{succ u2} R (f x) (f y)) -> (Eq.{succ u1} ι x y))
-Case conversion may be inaccurate. Consider using '#align polynomial.separable.inj_of_prod_X_sub_C Polynomial.Separable.inj_of_prod_X_sub_Cₓ'. -/
 theorem Separable.inj_of_prod_X_sub_C [Nontrivial R] {ι : Sort _} {f : ι → R} {s : Finset ι}
     (hfs : (∏ i in s, X - C (f i)).Separable) {x y : ι} (hx : x ∈ s) (hy : y ∈ s)
     (hfxy : f x = f y) : x = y := by
@@ -299,23 +242,11 @@ theorem Separable.inj_of_prod_X_sub_C [Nontrivial R] {ι : Sort _} {f : ι → R
   cases (hfs.of_mul_left.of_pow (not_is_unit_X_sub_C _) two_ne_zero).2
 #align polynomial.separable.inj_of_prod_X_sub_C Polynomial.Separable.inj_of_prod_X_sub_C
 
-/- warning: polynomial.separable.injective_of_prod_X_sub_C -> Polynomial.Separable.injective_of_prod_X_sub_C is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] {ι : Type.{u2}} [_inst_3 : Fintype.{u2} ι] {f : ι -> R}, (Polynomial.Separable.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Finset.prod.{u1, u2} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Finset.univ.{u2} ι _inst_3) (fun (i : ι) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (f i))))) -> (Function.Injective.{succ u2, succ u1} ι R f)
-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] [_inst_2 : Nontrivial.{u2} R] {ι : Type.{u1}} [_inst_3 : Fintype.{u1} ι] {f : ι -> R}, (Polynomial.Separable.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1) (Finset.prod.{u2, u1} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.commRing.{u2} R _inst_1)) (Finset.univ.{u1} ι _inst_3) (fun (i : ι) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (f i)) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (instHSub.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.sub.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Polynomial.X.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Polynomial.C.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (f i))))) -> (Function.Injective.{succ u1, succ u2} ι R f)
-Case conversion may be inaccurate. Consider using '#align polynomial.separable.injective_of_prod_X_sub_C Polynomial.Separable.injective_of_prod_X_sub_Cₓ'. -/
 theorem Separable.injective_of_prod_X_sub_C [Nontrivial R] {ι : Sort _} [Fintype ι] {f : ι → R}
     (hfs : (∏ i, X - C (f i)).Separable) : Function.Injective f := fun x y hfxy =>
   hfs.inj_of_prod_X_sub_C (mem_univ _) (mem_univ _) hfxy
 #align polynomial.separable.injective_of_prod_X_sub_C Polynomial.Separable.injective_of_prod_X_sub_C
 
-/- warning: polynomial.nodup_of_separable_prod -> Polynomial.nodup_of_separable_prod is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] {s : Multiset.{u1} R}, (Polynomial.Separable.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a)) s))) -> (Multiset.Nodup.{u1} R s)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] {s : Multiset.{u1} R}, (Polynomial.Separable.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a)) s))) -> (Multiset.Nodup.{u1} R s)
-Case conversion may be inaccurate. Consider using '#align polynomial.nodup_of_separable_prod Polynomial.nodup_of_separable_prodₓ'. -/
 theorem nodup_of_separable_prod [Nontrivial R] {s : Multiset R}
     (hs : Separable (Multiset.map (fun a => X - C a) s).Prod) : s.Nodup :=
   by
@@ -325,9 +256,6 @@ theorem nodup_of_separable_prod [Nontrivial R] {s : Multiset R}
   simpa only [Multiset.map_cons, Multiset.prod_cons] using mul_dvd_mul_left _ (dvd_mul_right _ _)
 #align polynomial.nodup_of_separable_prod Polynomial.nodup_of_separable_prod
 
-/- warning: polynomial.separable_X_pow_sub_C_unit -> Polynomial.separable_X_pow_sub_C_unit is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.separable_X_pow_sub_C_unit Polynomial.separable_X_pow_sub_C_unitₓ'. -/
 /-- If `is_unit n` in a `comm_ring R`, then `X ^ n - u` is separable for any unit `u`. -/
 theorem separable_X_pow_sub_C_unit {n : ℕ} (u : Rˣ) (hn : IsUnit (n : R)) :
     Separable (X ^ n - C (u : R)) := by
@@ -386,9 +314,6 @@ section Field
 
 variable {F : Type u} [Field F] {K : Type v} [Field K]
 
-/- warning: polynomial.separable_iff_derivative_ne_zero -> Polynomial.separable_iff_derivative_ne_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.separable_iff_derivative_ne_zero Polynomial.separable_iff_derivative_ne_zeroₓ'. -/
 theorem separable_iff_derivative_ne_zero {f : F[X]} (hf : Irreducible f) :
     f.Separable ↔ f.derivative ≠ 0 :=
   ⟨fun h1 h2 => hf.not_unit <| isCoprime_zero_right.1 <| h2 ▸ h1, fun h =>
@@ -405,9 +330,6 @@ theorem separable_map (f : F →+* K) {p : F[X]} : (p.map f).Separable ↔ p.Sep
 #align polynomial.separable_map Polynomial.separable_map
 -/
 
-/- warning: polynomial.separable_prod_X_sub_C_iff' -> Polynomial.separable_prod_X_sub_C_iff' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.separable_prod_X_sub_C_iff' Polynomial.separable_prod_X_sub_C_iff'ₓ'. -/
 theorem separable_prod_X_sub_C_iff' {ι : Sort _} {f : ι → F} {s : Finset ι} :
     (∏ i in s, X - C (f i)).Separable ↔ ∀ x ∈ s, ∀ y ∈ s, f x = f y → x = y :=
   ⟨fun hfs x hx y hy hfxy => hfs.inj_of_prod_X_sub_C hx hy hfxy, fun H => by rw [← prod_attach];
@@ -419,9 +341,6 @@ theorem separable_prod_X_sub_C_iff' {ι : Sort _} {f : ι → F} {s : Finset ι}
         fun _ _ => separable_X_sub_C⟩
 #align polynomial.separable_prod_X_sub_C_iff' Polynomial.separable_prod_X_sub_C_iff'
 
-/- warning: polynomial.separable_prod_X_sub_C_iff -> Polynomial.separable_prod_X_sub_C_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.separable_prod_X_sub_C_iff Polynomial.separable_prod_X_sub_C_iffₓ'. -/
 theorem separable_prod_X_sub_C_iff {ι : Sort _} [Fintype ι] {f : ι → F} :
     (∏ i, X - C (f i)).Separable ↔ Function.Injective f :=
   separable_prod_X_sub_C_iff'.trans <| by simp_rw [mem_univ, true_imp_iff, Function.Injective]
@@ -433,9 +352,6 @@ variable (p : ℕ) [HF : CharP F p]
 
 include HF
 
-/- warning: polynomial.separable_or -> Polynomial.separable_or is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.separable_or Polynomial.separable_orₓ'. -/
 theorem separable_or {f : F[X]} (hf : Irreducible f) :
     f.Separable ∨ ¬f.Separable ∧ ∃ g : F[X], Irreducible g ∧ expand F p g = f :=
   if H : f.derivative = 0 then by
@@ -453,9 +369,6 @@ theorem separable_or {f : F[X]} (hf : Irreducible f) :
   else Or.inl <| (separable_iff_derivative_ne_zero hf).2 H
 #align polynomial.separable_or Polynomial.separable_or
 
-/- warning: polynomial.exists_separable_of_irreducible -> Polynomial.exists_separable_of_irreducible is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.exists_separable_of_irreducible Polynomial.exists_separable_of_irreducibleₓ'. -/
 theorem exists_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : p ≠ 0) :
     ∃ (n : ℕ)(g : F[X]), g.Separable ∧ expand F (p ^ n) g = f :=
   by
@@ -478,9 +391,6 @@ theorem exists_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : p
     rw [← hgf, expand_expand, pow_succ]
 #align polynomial.exists_separable_of_irreducible Polynomial.exists_separable_of_irreducible
 
-/- warning: polynomial.is_unit_or_eq_zero_of_separable_expand -> Polynomial.isUnit_or_eq_zero_of_separable_expand is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.is_unit_or_eq_zero_of_separable_expand Polynomial.isUnit_or_eq_zero_of_separable_expandₓ'. -/
 theorem isUnit_or_eq_zero_of_separable_expand {f : F[X]} (n : ℕ) (hp : 0 < p)
     (hf : (expand F (p ^ n) f).Separable) : IsUnit f ∨ n = 0 :=
   by
@@ -495,9 +405,6 @@ theorem isUnit_or_eq_zero_of_separable_expand {f : F[X]} (n : ℕ) (hp : 0 < p)
   rwa [hrf, is_unit_C]
 #align polynomial.is_unit_or_eq_zero_of_separable_expand Polynomial.isUnit_or_eq_zero_of_separable_expand
 
-/- warning: polynomial.unique_separable_of_irreducible -> Polynomial.unique_separable_of_irreducible is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.unique_separable_of_irreducible Polynomial.unique_separable_of_irreducibleₓ'. -/
 theorem unique_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : 0 < p) (n₁ : ℕ)
     (g₁ : F[X]) (hg₁ : g₁.Separable) (hgf₁ : expand F (p ^ n₁) g₁ = f) (n₂ : ℕ) (g₂ : F[X])
     (hg₂ : g₂.Separable) (hgf₂ : expand F (p ^ n₂) g₂ = f) : n₁ = n₂ ∧ g₁ = g₂ :=
@@ -518,21 +425,12 @@ theorem unique_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : 0
 
 end CharP
 
-/- warning: polynomial.separable_X_pow_sub_C -> Polynomial.separable_X_pow_sub_C is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.separable_X_pow_sub_C Polynomial.separable_X_pow_sub_Cₓ'. -/
 /-- If `n ≠ 0` in `F`, then ` X ^ n - a` is separable for any `a ≠ 0`. -/
 theorem separable_X_pow_sub_C {n : ℕ} (a : F) (hn : (n : F) ≠ 0) (ha : a ≠ 0) :
     Separable (X ^ n - C a) :=
   separable_X_pow_sub_C_unit (Units.mk0 a ha) (IsUnit.mk0 n hn)
 #align polynomial.separable_X_pow_sub_C Polynomial.separable_X_pow_sub_C
 
-/- warning: polynomial.X_pow_sub_one_separable_iff -> Polynomial.X_pow_sub_one_separable_iff is a dubious translation:
-lean 3 declaration is
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {n : Nat}, Iff (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) Nat (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHPow.{u1, 0} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.X.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) n) (OfNat.ofNat.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 1 (OfNat.mk.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 1 (One.one.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.hasOne.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))) (Ne.{succ u1} F ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat F (HasLiftT.mk.{1, succ u1} Nat F (CoeTCₓ.coe.{1, succ u1} Nat F (Nat.castCoe.{u1} F (AddMonoidWithOne.toNatCast.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))) n) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))))))
-but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {n : Nat}, Iff (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) Nat (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHPow.{u1, 0} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Polynomial.X.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) n) (OfNat.ofNat.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.one.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Ne.{succ u1} F (Nat.cast.{u1} F (Semiring.toNatCast.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) n) (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (CommMonoidWithZero.toZero.{u1} F (CommGroupWithZero.toCommMonoidWithZero.{u1} F (Semifield.toCommGroupWithZero.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))
-Case conversion may be inaccurate. Consider using '#align polynomial.X_pow_sub_one_separable_iff Polynomial.X_pow_sub_one_separable_iffₓ'. -/
 -- this can possibly be strengthened to making `separable_X_pow_sub_C_unit` a
 -- bi-implication, but it is nontrivial!
 /-- In a field `F`, `X ^ n - 1` is separable iff `↑n ≠ 0`. -/
@@ -560,9 +458,6 @@ theorem card_rootSet_eq_natDegree [Algebra F K] {p : F[X]} (hsep : p.Separable)
 
 variable {i : F →+* K}
 
-/- warning: polynomial.eq_X_sub_C_of_separable_of_root_eq -> Polynomial.eq_X_sub_C_of_separable_of_root_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.eq_X_sub_C_of_separable_of_root_eq Polynomial.eq_X_sub_C_of_separable_of_root_eqₓ'. -/
 theorem eq_X_sub_C_of_separable_of_root_eq {x : F} {h : F[X]} (h_sep : h.Separable)
     (h_root : h.eval x = 0) (h_splits : Splits i h) (h_roots : ∀ y ∈ (h.map i).roots, y = i x) :
     h = C (leadingCoeff h) * (X - C x) :=
@@ -581,9 +476,6 @@ theorem eq_X_sub_C_of_separable_of_root_eq {x : F} {h : F[X]} (h_sep : h.Separab
   · exact nodup_roots (separable.map h_sep)
 #align polynomial.eq_X_sub_C_of_separable_of_root_eq Polynomial.eq_X_sub_C_of_separable_of_root_eq
 
-/- warning: polynomial.exists_finset_of_splits -> Polynomial.exists_finset_of_splits is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.exists_finset_of_splits Polynomial.exists_finset_of_splitsₓ'. -/
 theorem exists_finset_of_splits (i : F →+* K) {f : F[X]} (sep : Separable f) (sp : Splits i f) :
     ∃ s : Finset K, f.map i = C (i f.leadingCoeff) * s.Prod fun a : K => X - C a :=
   by
@@ -598,12 +490,6 @@ theorem exists_finset_of_splits (i : F →+* K) {f : F[X]} (sep : Separable f) (
 
 end Splits
 
-/- warning: irreducible.separable -> Irreducible.separable is a dubious translation:
-lean 3 declaration is
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] [_inst_3 : CharZero.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))] {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f) -> (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) f)
-but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] [_inst_3 : CharZero.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (Ring.toAddGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))] {f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) f) -> (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) f)
-Case conversion may be inaccurate. Consider using '#align irreducible.separable Irreducible.separableₓ'. -/
 theorem Irreducible.separable [CharZero F] {f : F[X]} (hf : Irreducible f) : f.Separable :=
   by
   rw [separable_iff_derivative_ne_zero hf, Ne, ← degree_eq_bot, degree_derivative_eq]
@@ -646,34 +532,16 @@ class IsSeparable : Prop where
 
 variable (F) {K}
 
-/- warning: is_separable.is_integral -> IsSeparable.isIntegral is a dubious translation:
-lean 3 declaration is
-  forall (F : Type.{u1}) {K : Type.{u2}} [_inst_1 : CommRing.{u1} F] [_inst_2 : Ring.{u2} K] [_inst_3 : Algebra.{u1, u2} F K (CommRing.toCommSemiring.{u1} F _inst_1) (Ring.toSemiring.{u2} K _inst_2)] [_inst_4 : IsSeparable.{u1, u2} F K _inst_1 _inst_2 _inst_3] (x : K), IsIntegral.{u1, u2} F K _inst_1 _inst_2 _inst_3 x
-but is expected to have type
-  forall (F : Type.{u2}) {K : Type.{u1}} [_inst_1 : CommRing.{u2} F] [_inst_2 : Ring.{u1} K] [_inst_3 : Algebra.{u2, u1} F K (CommRing.toCommSemiring.{u2} F _inst_1) (Ring.toSemiring.{u1} K _inst_2)] [_inst_4 : IsSeparable.{u2, u1} F K _inst_1 _inst_2 _inst_3] (x : K), IsIntegral.{u2, u1} F K _inst_1 _inst_2 _inst_3 x
-Case conversion may be inaccurate. Consider using '#align is_separable.is_integral IsSeparable.isIntegralₓ'. -/
 theorem IsSeparable.isIntegral [IsSeparable F K] : ∀ x : K, IsIntegral F x :=
   IsSeparable.is_integral'
 #align is_separable.is_integral IsSeparable.isIntegral
 
-/- warning: is_separable.separable -> IsSeparable.separable is a dubious translation:
-lean 3 declaration is
-  forall (F : Type.{u1}) {K : Type.{u2}} [_inst_1 : CommRing.{u1} F] [_inst_2 : Ring.{u2} K] [_inst_3 : Algebra.{u1, u2} F K (CommRing.toCommSemiring.{u1} F _inst_1) (Ring.toSemiring.{u2} K _inst_2)] [_inst_4 : IsSeparable.{u1, u2} F K _inst_1 _inst_2 _inst_3] (x : K), Polynomial.Separable.{u1} F (CommRing.toCommSemiring.{u1} F _inst_1) (minpoly.{u1, u2} F K _inst_1 _inst_2 _inst_3 x)
-but is expected to have type
-  forall (F : Type.{u2}) {K : Type.{u1}} [_inst_1 : CommRing.{u2} F] [_inst_2 : Ring.{u1} K] [_inst_3 : Algebra.{u2, u1} F K (CommRing.toCommSemiring.{u2} F _inst_1) (Ring.toSemiring.{u1} K _inst_2)] [_inst_4 : IsSeparable.{u2, u1} F K _inst_1 _inst_2 _inst_3] (x : K), Polynomial.Separable.{u2} F (CommRing.toCommSemiring.{u2} F _inst_1) (minpoly.{u2, u1} F K _inst_1 _inst_2 _inst_3 x)
-Case conversion may be inaccurate. Consider using '#align is_separable.separable IsSeparable.separableₓ'. -/
 theorem IsSeparable.separable [IsSeparable F K] : ∀ x : K, (minpoly F x).Separable :=
   IsSeparable.separable'
 #align is_separable.separable IsSeparable.separable
 
 variable {F K}
 
-/- warning: is_separable_iff -> isSeparable_iff is a dubious translation:
-lean 3 declaration is
-  forall {F : Type.{u1}} {K : Type.{u2}} [_inst_1 : CommRing.{u1} F] [_inst_2 : Ring.{u2} K] [_inst_3 : Algebra.{u1, u2} F K (CommRing.toCommSemiring.{u1} F _inst_1) (Ring.toSemiring.{u2} K _inst_2)], Iff (IsSeparable.{u1, u2} F K _inst_1 _inst_2 _inst_3) (forall (x : K), And (IsIntegral.{u1, u2} F K _inst_1 _inst_2 _inst_3 x) (Polynomial.Separable.{u1} F (CommRing.toCommSemiring.{u1} F _inst_1) (minpoly.{u1, u2} F K _inst_1 _inst_2 _inst_3 x)))
-but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} [_inst_1 : CommRing.{u2} F] [_inst_2 : Ring.{u1} K] [_inst_3 : Algebra.{u2, u1} F K (CommRing.toCommSemiring.{u2} F _inst_1) (Ring.toSemiring.{u1} K _inst_2)], Iff (IsSeparable.{u2, u1} F K _inst_1 _inst_2 _inst_3) (forall (x : K), And (IsIntegral.{u2, u1} F K _inst_1 _inst_2 _inst_3 x) (Polynomial.Separable.{u2} F (CommRing.toCommSemiring.{u2} F _inst_1) (minpoly.{u2, u1} F K _inst_1 _inst_2 _inst_3 x)))
-Case conversion may be inaccurate. Consider using '#align is_separable_iff isSeparable_iffₓ'. -/
 theorem isSeparable_iff : IsSeparable F K ↔ ∀ x : K, IsIntegral F x ∧ (minpoly F x).Separable :=
   ⟨fun h x => ⟨@IsSeparable.isIntegral F _ _ _ h x, @IsSeparable.separable F _ _ _ h x⟩, fun h =>
     ⟨fun x => (h x).1, fun x => (h x).2⟩⟩
@@ -687,12 +555,6 @@ instance isSeparable_self (F : Type _) [Field F] : IsSeparable F F :=
 #align is_separable_self isSeparable_self
 -/
 
-/- warning: is_separable.of_finite -> IsSeparable.of_finite is a dubious translation:
-lean 3 declaration is
-  forall (F : Type.{u1}) (K : Type.{u2}) [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] [_inst_3 : Algebra.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))] [_inst_4 : FiniteDimensional.{u1, u2} F K (Field.toDivisionRing.{u1} F _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (Algebra.toModule.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) _inst_3)] [_inst_5 : CharZero.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))], IsSeparable.{u1, u2} F K (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)) (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)) _inst_3
-but is expected to have type
-  forall (F : Type.{u1}) (K : Type.{u2}) [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] [_inst_3 : Algebra.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))] [_inst_4 : FiniteDimensional.{u1, u2} F K (Field.toDivisionRing.{u1} F _inst_1) (Ring.toAddCommGroup.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) (Algebra.toModule.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))) _inst_3)] [_inst_5 : CharZero.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (Ring.toAddGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))], IsSeparable.{u1, u2} F K (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)) (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)) _inst_3
-Case conversion may be inaccurate. Consider using '#align is_separable.of_finite IsSeparable.of_finiteₓ'. -/
 -- See note [lower instance priority]
 /-- A finite field extension in characteristic 0 is separable. -/
 instance (priority := 100) IsSeparable.of_finite (F K : Type _) [Field F] [Field K] [Algebra F K]
@@ -706,23 +568,11 @@ section IsSeparableTower
 variable (F K E : Type _) [Field F] [Field K] [Field E] [Algebra F K] [Algebra F E] [Algebra K E]
   [IsScalarTower F K E]
 
-/- warning: is_separable_tower_top_of_is_separable -> isSeparable_tower_top_of_isSeparable is a dubious translation:
-lean 3 declaration is
-  forall (F : Type.{u1}) (K : Type.{u2}) (E : Type.{u3}) [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] [_inst_3 : Field.{u3} E] [_inst_4 : Algebra.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))] [_inst_5 : Algebra.{u1, u3} F E (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3)))] [_inst_6 : Algebra.{u2, u3} K E (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)) (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3)))] [_inst_7 : IsScalarTower.{u1, u2, u3} F K E (SMulZeroClass.toHasSmul.{u1, u2} F K (AddZeroClass.toHasZero.{u2} K (AddMonoid.toAddZeroClass.{u2} K (AddCommMonoid.toAddMonoid.{u2} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} F K (MulZeroClass.toHasZero.{u1} F (MulZeroOneClass.toMulZeroClass.{u1} F (MonoidWithZero.toMulZeroOneClass.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (AddZeroClass.toHasZero.{u2} K (AddMonoid.toAddZeroClass.{u2} K (AddCommMonoid.toAddMonoid.{u2} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} F K (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddZeroClass.toHasZero.{u2} K (AddMonoid.toAddZeroClass.{u2} K (AddCommMonoid.toAddMonoid.{u2} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))))) (Module.toMulActionWithZero.{u1, u2} F K (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (Algebra.toModule.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} K E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))))))))) (SMulWithZero.toSmulZeroClass.{u2, u3} K E (MulZeroClass.toHasZero.{u2} K (MulZeroOneClass.toMulZeroClass.{u2} K (MonoidWithZero.toMulZeroOneClass.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))))))))) (MulActionWithZero.toSMulWithZero.{u2, u3} K E (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))))))))) (Module.toMulActionWithZero.{u2, u3} K E (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3)))))) (Algebra.toModule.{u2, u3} K E (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)) (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} F E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} F E (MulZeroClass.toHasZero.{u1} F (MulZeroOneClass.toMulZeroClass.{u1} F (MonoidWithZero.toMulZeroOneClass.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} F E (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))))))))) (Module.toMulActionWithZero.{u1, u3} F E (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3)))))) (Algebra.toModule.{u1, u3} F E (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))) _inst_5)))))] [_inst_8 : IsSeparable.{u1, u3} F E (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)) (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3)) _inst_5], IsSeparable.{u2, u3} K E (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3)) _inst_6
-but is expected to have type
-  forall (F : Type.{u3}) (K : Type.{u1}) (E : Type.{u2}) [_inst_1 : Field.{u3} F] [_inst_2 : Field.{u1} K] [_inst_3 : Field.{u2} E] [_inst_4 : Algebra.{u3, u1} F K (Semifield.toCommSemiring.{u3} F (Field.toSemifield.{u3} F _inst_1)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))] [_inst_5 : Algebra.{u3, u2} F E (Semifield.toCommSemiring.{u3} F (Field.toSemifield.{u3} F _inst_1)) (DivisionSemiring.toSemiring.{u2} E (Semifield.toDivisionSemiring.{u2} E (Field.toSemifield.{u2} E _inst_3)))] [_inst_6 : Algebra.{u1, u2} K E (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)) (DivisionSemiring.toSemiring.{u2} E (Semifield.toDivisionSemiring.{u2} E (Field.toSemifield.{u2} E _inst_3)))] [_inst_7 : IsScalarTower.{u3, u1, u2} F K E (Algebra.toSMul.{u3, u1} F K (Semifield.toCommSemiring.{u3} F (Field.toSemifield.{u3} F _inst_1)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) _inst_4) (Algebra.toSMul.{u1, u2} K E (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)) (DivisionSemiring.toSemiring.{u2} E (Semifield.toDivisionSemiring.{u2} E (Field.toSemifield.{u2} E _inst_3))) _inst_6) (Algebra.toSMul.{u3, u2} F E (Semifield.toCommSemiring.{u3} F (Field.toSemifield.{u3} F _inst_1)) (DivisionSemiring.toSemiring.{u2} E (Semifield.toDivisionSemiring.{u2} E (Field.toSemifield.{u2} E _inst_3))) _inst_5)] [_inst_8 : IsSeparable.{u3, u2} F E (EuclideanDomain.toCommRing.{u3} F (Field.toEuclideanDomain.{u3} F _inst_1)) (DivisionRing.toRing.{u2} E (Field.toDivisionRing.{u2} E _inst_3)) _inst_5], IsSeparable.{u1, u2} K E (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (DivisionRing.toRing.{u2} E (Field.toDivisionRing.{u2} E _inst_3)) _inst_6
-Case conversion may be inaccurate. Consider using '#align is_separable_tower_top_of_is_separable isSeparable_tower_top_of_isSeparableₓ'. -/
 theorem isSeparable_tower_top_of_isSeparable [IsSeparable F E] : IsSeparable K E :=
   ⟨fun x => isIntegral_of_isScalarTower (IsSeparable.isIntegral F x), fun x =>
     (IsSeparable.separable F x).map.of_dvd (minpoly.dvd_map_of_isScalarTower _ _ _)⟩
 #align is_separable_tower_top_of_is_separable isSeparable_tower_top_of_isSeparable
 
-/- warning: is_separable_tower_bot_of_is_separable -> isSeparable_tower_bot_of_isSeparable is a dubious translation:
-lean 3 declaration is
-  forall (F : Type.{u1}) (K : Type.{u2}) (E : Type.{u3}) [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] [_inst_3 : Field.{u3} E] [_inst_4 : Algebra.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))] [_inst_5 : Algebra.{u1, u3} F E (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3)))] [_inst_6 : Algebra.{u2, u3} K E (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)) (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3)))] [_inst_7 : IsScalarTower.{u1, u2, u3} F K E (SMulZeroClass.toHasSmul.{u1, u2} F K (AddZeroClass.toHasZero.{u2} K (AddMonoid.toAddZeroClass.{u2} K (AddCommMonoid.toAddMonoid.{u2} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} F K (MulZeroClass.toHasZero.{u1} F (MulZeroOneClass.toMulZeroClass.{u1} F (MonoidWithZero.toMulZeroOneClass.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (AddZeroClass.toHasZero.{u2} K (AddMonoid.toAddZeroClass.{u2} K (AddCommMonoid.toAddMonoid.{u2} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} F K (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddZeroClass.toHasZero.{u2} K (AddMonoid.toAddZeroClass.{u2} K (AddCommMonoid.toAddMonoid.{u2} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))))) (Module.toMulActionWithZero.{u1, u2} F K (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (Algebra.toModule.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} K E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))))))))) (SMulWithZero.toSmulZeroClass.{u2, u3} K E (MulZeroClass.toHasZero.{u2} K (MulZeroOneClass.toMulZeroClass.{u2} K (MonoidWithZero.toMulZeroOneClass.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))))))))) (MulActionWithZero.toSMulWithZero.{u2, u3} K E (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))))))))) (Module.toMulActionWithZero.{u2, u3} K E (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3)))))) (Algebra.toModule.{u2, u3} K E (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)) (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} F E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} F E (MulZeroClass.toHasZero.{u1} F (MulZeroOneClass.toMulZeroClass.{u1} F (MonoidWithZero.toMulZeroOneClass.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} F E (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))))))))) (Module.toMulActionWithZero.{u1, u3} F E (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3)))))) (Algebra.toModule.{u1, u3} F E (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))) _inst_5)))))] [h : IsSeparable.{u1, u3} F E (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)) (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3)) _inst_5], IsSeparable.{u1, u2} F K (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)) (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)) _inst_4
-but is expected to have type
-  forall (F : Type.{u3}) (K : Type.{u1}) (E : Type.{u2}) [_inst_1 : Field.{u3} F] [_inst_2 : Field.{u1} K] [_inst_3 : Field.{u2} E] [_inst_4 : Algebra.{u3, u1} F K (Semifield.toCommSemiring.{u3} F (Field.toSemifield.{u3} F _inst_1)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))] [_inst_5 : Algebra.{u3, u2} F E (Semifield.toCommSemiring.{u3} F (Field.toSemifield.{u3} F _inst_1)) (DivisionSemiring.toSemiring.{u2} E (Semifield.toDivisionSemiring.{u2} E (Field.toSemifield.{u2} E _inst_3)))] [_inst_6 : Algebra.{u1, u2} K E (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)) (DivisionSemiring.toSemiring.{u2} E (Semifield.toDivisionSemiring.{u2} E (Field.toSemifield.{u2} E _inst_3)))] [_inst_7 : IsScalarTower.{u3, u1, u2} F K E (Algebra.toSMul.{u3, u1} F K (Semifield.toCommSemiring.{u3} F (Field.toSemifield.{u3} F _inst_1)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) _inst_4) (Algebra.toSMul.{u1, u2} K E (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)) (DivisionSemiring.toSemiring.{u2} E (Semifield.toDivisionSemiring.{u2} E (Field.toSemifield.{u2} E _inst_3))) _inst_6) (Algebra.toSMul.{u3, u2} F E (Semifield.toCommSemiring.{u3} F (Field.toSemifield.{u3} F _inst_1)) (DivisionSemiring.toSemiring.{u2} E (Semifield.toDivisionSemiring.{u2} E (Field.toSemifield.{u2} E _inst_3))) _inst_5)] [h : IsSeparable.{u3, u2} F E (EuclideanDomain.toCommRing.{u3} F (Field.toEuclideanDomain.{u3} F _inst_1)) (DivisionRing.toRing.{u2} E (Field.toDivisionRing.{u2} E _inst_3)) _inst_5], IsSeparable.{u3, u1} F K (EuclideanDomain.toCommRing.{u3} F (Field.toEuclideanDomain.{u3} F _inst_1)) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)) _inst_4
-Case conversion may be inaccurate. Consider using '#align is_separable_tower_bot_of_is_separable isSeparable_tower_bot_of_isSeparableₓ'. -/
 theorem isSeparable_tower_bot_of_isSeparable [h : IsSeparable F E] : IsSeparable F K :=
   isSeparable_iff.2 fun x =>
     by
@@ -738,12 +588,6 @@ theorem isSeparable_tower_bot_of_isSeparable [h : IsSeparable F E] : IsSeparable
 
 variable {E}
 
-/- warning: is_separable.of_alg_hom -> IsSeparable.of_algHom is a dubious translation:
-lean 3 declaration is
-  forall (F : Type.{u1}) {E : Type.{u2}} [_inst_1 : Field.{u1} F] [_inst_3 : Field.{u2} E] [_inst_5 : Algebra.{u1, u2} F E (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Ring.toSemiring.{u2} E (DivisionRing.toRing.{u2} E (Field.toDivisionRing.{u2} E _inst_3)))] (E' : Type.{u3}) [_inst_8 : Field.{u3} E'] [_inst_9 : Algebra.{u1, u3} F E' (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Ring.toSemiring.{u3} E' (DivisionRing.toRing.{u3} E' (Field.toDivisionRing.{u3} E' _inst_8)))], (AlgHom.{u1, u2, u3} F E E' (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Ring.toSemiring.{u2} E (DivisionRing.toRing.{u2} E (Field.toDivisionRing.{u2} E _inst_3))) (Ring.toSemiring.{u3} E' (DivisionRing.toRing.{u3} E' (Field.toDivisionRing.{u3} E' _inst_8))) _inst_5 _inst_9) -> (forall [_inst_10 : IsSeparable.{u1, u3} F E' (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)) (DivisionRing.toRing.{u3} E' (Field.toDivisionRing.{u3} E' _inst_8)) _inst_9], IsSeparable.{u1, u2} F E (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)) (DivisionRing.toRing.{u2} E (Field.toDivisionRing.{u2} E _inst_3)) _inst_5)
-but is expected to have type
-  forall (F : Type.{u2}) {E : Type.{u1}} [_inst_1 : Field.{u2} F] [_inst_3 : Field.{u1} E] [_inst_5 : Algebra.{u2, u1} F E (Semifield.toCommSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)) (DivisionSemiring.toSemiring.{u1} E (Semifield.toDivisionSemiring.{u1} E (Field.toSemifield.{u1} E _inst_3)))] (E' : Type.{u3}) [_inst_8 : Field.{u3} E'] [_inst_9 : Algebra.{u2, u3} F E' (Semifield.toCommSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)) (DivisionSemiring.toSemiring.{u3} E' (Semifield.toDivisionSemiring.{u3} E' (Field.toSemifield.{u3} E' _inst_8)))], (AlgHom.{u2, u1, u3} F E E' (Semifield.toCommSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)) (DivisionSemiring.toSemiring.{u1} E (Semifield.toDivisionSemiring.{u1} E (Field.toSemifield.{u1} E _inst_3))) (DivisionSemiring.toSemiring.{u3} E' (Semifield.toDivisionSemiring.{u3} E' (Field.toSemifield.{u3} E' _inst_8))) _inst_5 _inst_9) -> (forall [_inst_10 : IsSeparable.{u2, u3} F E' (EuclideanDomain.toCommRing.{u2} F (Field.toEuclideanDomain.{u2} F _inst_1)) (DivisionRing.toRing.{u3} E' (Field.toDivisionRing.{u3} E' _inst_8)) _inst_9], IsSeparable.{u2, u1} F E (EuclideanDomain.toCommRing.{u2} F (Field.toEuclideanDomain.{u2} F _inst_1)) (DivisionRing.toRing.{u1} E (Field.toDivisionRing.{u1} E _inst_3)) _inst_5)
-Case conversion may be inaccurate. Consider using '#align is_separable.of_alg_hom IsSeparable.of_algHomₓ'. -/
 theorem IsSeparable.of_algHom (E' : Type _) [Field E'] [Algebra F E'] (f : E →ₐ[F] E')
     [IsSeparable F E'] : IsSeparable F E :=
   by
@@ -762,12 +606,6 @@ variable {K L F : Type _} [Field K] [Field L] [Field F]
 
 variable [Algebra K S] [Algebra K L]
 
-/- warning: alg_hom.card_of_power_basis -> AlgHom.card_of_powerBasis is a dubious translation:
-lean 3 declaration is
-  forall {S : Type.{u1}} [_inst_1 : CommRing.{u1} S] {K : Type.{u2}} {L : Type.{u3}} [_inst_2 : Field.{u2} K] [_inst_3 : Field.{u3} L] [_inst_5 : Algebra.{u2, u1} K S (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_1))] [_inst_6 : Algebra.{u2, u3} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)) (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_3)))] (pb : PowerBasis.{u2, u1} K S (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (CommRing.toRing.{u1} S _inst_1) _inst_5), (Polynomial.Separable.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)) (minpoly.{u2, u1} K S (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (CommRing.toRing.{u1} S _inst_1) _inst_5 (PowerBasis.gen.{u2, u1} K S (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (CommRing.toRing.{u1} S _inst_1) _inst_5 pb))) -> (Polynomial.Splits.{u2, u3} K L (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) _inst_3 (algebraMap.{u2, u3} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)) (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_3))) _inst_6) (minpoly.{u2, u1} K S (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (CommRing.toRing.{u1} S _inst_1) _inst_5 (PowerBasis.gen.{u2, u1} K S (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (CommRing.toRing.{u1} S _inst_1) _inst_5 pb))) -> (Eq.{1} Nat (Fintype.card.{max u1 u3} (AlgHom.{u2, u1, u3} K S L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_1)) (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_3))) _inst_5 _inst_6) (PowerBasis.AlgHom.fintype.{u1, u2, u3} S (CommRing.toRing.{u1} S _inst_1) K L (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (EuclideanDomain.toCommRing.{u3} L (Field.toEuclideanDomain.{u3} L _inst_3)) (Field.isDomain.{u3} L _inst_3) _inst_6 _inst_5 pb)) (PowerBasis.dim.{u2, u1} K S (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (CommRing.toRing.{u1} S _inst_1) _inst_5 pb))
-but is expected to have type
-  forall {S : Type.{u2}} [_inst_1 : CommRing.{u2} S] {K : Type.{u3}} {L : Type.{u1}} [_inst_2 : Field.{u3} K] [_inst_3 : Field.{u1} L] [_inst_5 : Algebra.{u3, u2} K S (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_2)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_1))] [_inst_6 : Algebra.{u3, u1} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_2)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_3)))] (pb : PowerBasis.{u3, u2} K S (EuclideanDomain.toCommRing.{u3} K (Field.toEuclideanDomain.{u3} K _inst_2)) (CommRing.toRing.{u2} S _inst_1) _inst_5), (Polynomial.Separable.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_2)) (minpoly.{u3, u2} K S (EuclideanDomain.toCommRing.{u3} K (Field.toEuclideanDomain.{u3} K _inst_2)) (CommRing.toRing.{u2} S _inst_1) _inst_5 (PowerBasis.gen.{u3, u2} K S (EuclideanDomain.toCommRing.{u3} K (Field.toEuclideanDomain.{u3} K _inst_2)) (CommRing.toRing.{u2} S _inst_1) _inst_5 pb))) -> (Polynomial.Splits.{u3, u1} K L (EuclideanDomain.toCommRing.{u3} K (Field.toEuclideanDomain.{u3} K _inst_2)) _inst_3 (algebraMap.{u3, u1} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_2)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_3))) _inst_6) (minpoly.{u3, u2} K S (EuclideanDomain.toCommRing.{u3} K (Field.toEuclideanDomain.{u3} K _inst_2)) (CommRing.toRing.{u2} S _inst_1) _inst_5 (PowerBasis.gen.{u3, u2} K S (EuclideanDomain.toCommRing.{u3} K (Field.toEuclideanDomain.{u3} K _inst_2)) (CommRing.toRing.{u2} S _inst_1) _inst_5 pb))) -> (Eq.{1} Nat (Fintype.card.{max u1 u2} (AlgHom.{u3, u2, u1} K S L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_2)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_3))) _inst_5 _inst_6) (PowerBasis.AlgHom.fintype.{u2, u3, u1} S (CommRing.toRing.{u2} S _inst_1) K L (EuclideanDomain.toCommRing.{u3} K (Field.toEuclideanDomain.{u3} K _inst_2)) (EuclideanDomain.toCommRing.{u1} L (Field.toEuclideanDomain.{u1} L _inst_3)) (Field.isDomain.{u1} L _inst_3) _inst_6 _inst_5 pb)) (PowerBasis.dim.{u3, u2} K S (EuclideanDomain.toCommRing.{u3} K (Field.toEuclideanDomain.{u3} K _inst_2)) (CommRing.toRing.{u2} S _inst_1) _inst_5 pb))
-Case conversion may be inaccurate. Consider using '#align alg_hom.card_of_power_basis AlgHom.card_of_powerBasisₓ'. -/
 theorem AlgHom.card_of_powerBasis (pb : PowerBasis K S) (h_sep : (minpoly K pb.gen).Separable)
     (h_splits : (minpoly K pb.gen).Splits (algebraMap K L)) :
     @Fintype.card (S →ₐ[K] L) (PowerBasis.AlgHom.fintype pb) = pb.dim :=

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

@@ -100,9 +100,7 @@ theorem separable_X_add_C (a : R) : (X + C a).Separable :=
 #align polynomial.separable_X_add_C Polynomial.separable_X_add_C
 
 #print Polynomial.separable_X /-
-theorem separable_X : (X : R[X]).Separable :=
-  by
-  rw [separable_def, derivative_X]
+theorem separable_X : (X : R[X]).Separable := by rw [separable_def, derivative_X];
   exact isCoprime_one_right
 #align polynomial.separable_X Polynomial.separable_X
 -/
@@ -126,18 +124,14 @@ theorem Separable.of_mul_left {f g : R[X]} (h : (f * g).Separable) : f.Separable
 -/
 
 #print Polynomial.Separable.of_mul_right /-
-theorem Separable.of_mul_right {f g : R[X]} (h : (f * g).Separable) : g.Separable :=
-  by
-  rw [mul_comm] at h
-  exact h.of_mul_left
+theorem Separable.of_mul_right {f g : R[X]} (h : (f * g).Separable) : g.Separable := by
+  rw [mul_comm] at h; exact h.of_mul_left
 #align polynomial.separable.of_mul_right Polynomial.Separable.of_mul_right
 -/
 
 #print Polynomial.Separable.of_dvd /-
-theorem Separable.of_dvd {f g : R[X]} (hf : f.Separable) (hfg : g ∣ f) : g.Separable :=
-  by
-  rcases hfg with ⟨f', rfl⟩
-  exact separable.of_mul_left hf
+theorem Separable.of_dvd {f g : R[X]} (hf : f.Separable) (hfg : g ∣ f) : g.Separable := by
+  rcases hfg with ⟨f', rfl⟩; exact separable.of_mul_left hf
 #align polynomial.separable.of_dvd Polynomial.Separable.of_dvd
 -/
 
@@ -255,8 +249,7 @@ theorem separable_X_sub_C {x : R} : Separable (X - C x) := by
 
 #print Polynomial.Separable.mul /-
 theorem Separable.mul {f g : R[X]} (hf : f.Separable) (hg : g.Separable) (h : IsCoprime f g) :
-    (f * g).Separable := by
-  rw [separable_def, derivative_mul]
+    (f * g).Separable := by rw [separable_def, derivative_mul];
   exact
     ((hf.mul_right h).add_mul_left_right _).mul_left ((h.symm.mul_right hg).mul_add_right_right _)
 #align polynomial.separable.mul Polynomial.Separable.mul
@@ -348,9 +341,7 @@ theorem separable_X_pow_sub_C_unit {n : ℕ} (u : Rˣ) (hn : IsUnit (n : R)) :
   calc
     -C ↑u⁻¹ * (X ^ n - C ↑u) + C ↑u⁻¹ * C n' * X * (↑n * X ^ (n - 1)) =
         C (↑u⁻¹ * ↑u) - C ↑u⁻¹ * X ^ n + C ↑u⁻¹ * C (n' * ↑n) * (X * X ^ (n - 1)) :=
-      by
-      simp only [C.map_mul, C_eq_nat_cast]
-      ring
+      by simp only [C.map_mul, C_eq_nat_cast]; ring
     _ = 1 := by
       simp only [Units.inv_mul, hn', C.map_one, mul_one, ← pow_succ,
         Nat.sub_add_cancel (show 1 ≤ n from hpos), sub_add_cancel]
@@ -403,9 +394,7 @@ theorem separable_iff_derivative_ne_zero {f : F[X]} (hf : Irreducible f) :
   ⟨fun h1 h2 => hf.not_unit <| isCoprime_zero_right.1 <| h2 ▸ h1, fun h =>
     EuclideanDomain.isCoprime_of_dvd (mt And.right h) fun g hg1 hg2 ⟨p, hg3⟩ hg4 =>
       let ⟨u, hu⟩ := (hf.isUnit_or_isUnit hg3).resolve_left hg1
-      have : f ∣ f.derivative := by
-        conv_lhs => rw [hg3, ← hu]
-        rwa [Units.mul_right_dvd]
+      have : f ∣ f.derivative := by conv_lhs => rw [hg3, ← hu]; rwa [Units.mul_right_dvd]
       not_lt_of_le (natDegree_le_of_dvd this h) <|
         natDegree_derivative_lt <| mt derivative_of_natDegree_zero h⟩
 #align polynomial.separable_iff_derivative_ne_zero Polynomial.separable_iff_derivative_ne_zero
@@ -421,9 +410,7 @@ theorem separable_map (f : F →+* K) {p : F[X]} : (p.map f).Separable ↔ p.Sep
 Case conversion may be inaccurate. Consider using '#align polynomial.separable_prod_X_sub_C_iff' Polynomial.separable_prod_X_sub_C_iff'ₓ'. -/
 theorem separable_prod_X_sub_C_iff' {ι : Sort _} {f : ι → F} {s : Finset ι} :
     (∏ i in s, X - C (f i)).Separable ↔ ∀ x ∈ s, ∀ y ∈ s, f x = f y → x = y :=
-  ⟨fun hfs x hx y hy hfxy => hfs.inj_of_prod_X_sub_C hx hy hfxy, fun H =>
-    by
-    rw [← prod_attach]
+  ⟨fun hfs x hx y hy hfxy => hfs.inj_of_prod_X_sub_C hx hy hfxy, fun H => by rw [← prod_attach];
     exact
       separable_prod'
         (fun x hx y hy hxy =>
@@ -475,25 +462,19 @@ theorem exists_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : p
   replace hp : p.prime := (CharP.char_is_prime_or_zero F p).resolve_right hp
   induction' hn : f.nat_degree using Nat.strong_induction_on with N ih generalizing f
   rcases separable_or p hf with (h | ⟨h1, g, hg, hgf⟩)
-  · refine' ⟨0, f, h, _⟩
-    rw [pow_zero, expand_one]
+  · refine' ⟨0, f, h, _⟩; rw [pow_zero, expand_one]
   · cases' N with N
     · rw [nat_degree_eq_zero_iff_degree_le_zero, degree_le_zero_iff] at hn
       rw [hn, separable_C, isUnit_iff_ne_zero, Classical.not_not] at h1
       have hf0 : f ≠ 0 := hf.ne_zero
-      rw [h1, C_0] at hn
-      exact absurd hn hf0
+      rw [h1, C_0] at hn; exact absurd hn hf0
     have hg1 : g.nat_degree * p = N.succ := by rwa [← nat_degree_expand, hgf]
-    have hg2 : g.nat_degree ≠ 0 := by
-      intro this
-      rw [this, MulZeroClass.zero_mul] at hg1
-      cases hg1
+    have hg2 : g.nat_degree ≠ 0 := by intro this; rw [this, MulZeroClass.zero_mul] at hg1; cases hg1
     have hg3 : g.nat_degree < N.succ :=
       by
       rw [← mul_one g.nat_degree, ← hg1]
       exact Nat.mul_lt_mul_of_pos_left hp.one_lt hg2.bot_lt
-    rcases ih _ hg3 hg rfl with ⟨n, g, hg4, rfl⟩
-    refine' ⟨n + 1, g, hg4, _⟩
+    rcases ih _ hg3 hg rfl with ⟨n, g, hg4, rfl⟩; refine' ⟨n + 1, g, hg4, _⟩
     rw [← hgf, expand_expand, pow_succ]
 #align polynomial.exists_separable_of_irreducible Polynomial.exists_separable_of_irreducible
 
@@ -526,19 +507,13 @@ theorem unique_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : 0
   · intro g₁ g₂ hg₁ Hg₁ hg₂ Hg₂
     simpa only [eq_comm] using this hf hp n₂ n₁ (le_of_not_le hn) g₂ g₁ hg₂ Hg₂ hg₁ Hg₁
   have hf0 : f ≠ 0 := hf.ne_zero
-  intros
-  rw [le_iff_exists_add] at hn
-  rcases hn with ⟨k, rfl⟩
-  rw [← hgf₁, pow_add, expand_mul, expand_inj (pow_pos hp n₁)] at hgf₂
-  subst hgf₂
+  intros ; rw [le_iff_exists_add] at hn; rcases hn with ⟨k, rfl⟩
+  rw [← hgf₁, pow_add, expand_mul, expand_inj (pow_pos hp n₁)] at hgf₂; subst hgf₂
   subst hgf₁
   rcases is_unit_or_eq_zero_of_separable_expand p k hp hg₁ with (h | rfl)
-  · rw [is_unit_iff] at h
-    rcases h with ⟨r, hr, rfl⟩
-    simp_rw [expand_C] at hf
-    exact absurd (is_unit_C.2 hr) hf.1
-  · rw [add_zero, pow_zero, expand_one]
-    constructor <;> rfl
+  · rw [is_unit_iff] at h; rcases h with ⟨r, hr, rfl⟩
+    simp_rw [expand_C] at hf; exact absurd (is_unit_C.2 hr) hf.1
+  · rw [add_zero, pow_zero, expand_one]; constructor <;> rfl
 #align polynomial.unique_separable_of_irreducible Polynomial.unique_separable_of_irreducible
 
 end CharP
@@ -592,9 +567,7 @@ theorem eq_X_sub_C_of_separable_of_root_eq {x : F} {h : F[X]} (h_sep : h.Separab
     (h_root : h.eval x = 0) (h_splits : Splits i h) (h_roots : ∀ y ∈ (h.map i).roots, y = i x) :
     h = C (leadingCoeff h) * (X - C x) :=
   by
-  have h_ne_zero : h ≠ 0 := by
-    rintro rfl
-    exact not_separable_zero h_sep
+  have h_ne_zero : h ≠ 0 := by rintro rfl; exact not_separable_zero h_sep
   apply Polynomial.eq_X_sub_C_of_splits_of_single_root i h_splits
   apply Finset.mk.inj
   · change _ = {i x}
@@ -710,10 +683,7 @@ end CommRing
 
 #print isSeparable_self /-
 instance isSeparable_self (F : Type _) [Field F] : IsSeparable F F :=
-  ⟨fun x => isIntegral_algebraMap, fun x =>
-    by
-    rw [minpoly.eq_X_sub_C']
-    exact separable_X_sub_C⟩
+  ⟨fun x => isIntegral_algebraMap, fun x => by rw [minpoly.eq_X_sub_C']; exact separable_X_sub_C⟩
 #align is_separable_self isSeparable_self
 -/
 

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

@@ -61,10 +61,7 @@ theorem separable_def (f : R[X]) : f.Separable ↔ IsCoprime f f.derivative :=
 #align polynomial.separable_def Polynomial.separable_def
 
 /- warning: polynomial.separable_def' -> Polynomial.separable_def' is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Iff (Polynomial.Separable.{u1} R _inst_1 f) (Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (a : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (b : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) a f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) b (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) f))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 1 (One.one.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.hasOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Iff (Polynomial.Separable.{u1} R _inst_1 f) (Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (a : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (b : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) a f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) f) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) b (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) f))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.separable_def' Polynomial.separable_def'ₓ'. -/
 theorem separable_def' (f : R[X]) : f.Separable ↔ ∃ a b : R[X], a * f + b * f.derivative = 1 :=
   Iff.rfl
@@ -336,10 +333,7 @@ theorem nodup_of_separable_prod [Nontrivial R] {s : Multiset R}
 #align polynomial.nodup_of_separable_prod Polynomial.nodup_of_separable_prod
 
 /- warning: polynomial.separable_X_pow_sub_C_unit -> Polynomial.separable_X_pow_sub_C_unit is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {n : Nat} (u : Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1))), (IsUnit.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) n)) -> (Polynomial.Separable.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (coeBase.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Units.hasCoe.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) u))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {n : Nat} (u : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))), (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n)) -> (Polynomial.Separable.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) u)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) u))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.separable_X_pow_sub_C_unit Polynomial.separable_X_pow_sub_C_unitₓ'. -/
 /-- If `is_unit n` in a `comm_ring R`, then `X ^ n - u` is separable for any unit `u`. -/
 theorem separable_X_pow_sub_C_unit {n : ℕ} (u : Rˣ) (hn : IsUnit (n : R)) :
@@ -402,10 +396,7 @@ section Field
 variable {F : Type u} [Field F] {K : Type v} [Field K]
 
 /- warning: polynomial.separable_iff_derivative_ne_zero -> Polynomial.separable_iff_derivative_ne_zero is a dubious translation:
-lean 3 declaration is
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f) -> (Iff (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) f) (Ne.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} F F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.derivative.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f) (OfNat.ofNat.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.zero.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))))
-but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) f) -> (Iff (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) f) (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} F F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Polynomial.derivative.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) f) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) f) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) f) (Polynomial.zero.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.separable_iff_derivative_ne_zero Polynomial.separable_iff_derivative_ne_zeroₓ'. -/
 theorem separable_iff_derivative_ne_zero {f : F[X]} (hf : Irreducible f) :
     f.Separable ↔ f.derivative ≠ 0 :=
@@ -426,10 +417,7 @@ theorem separable_map (f : F →+* K) {p : F[X]} : (p.map f).Separable ↔ p.Sep
 -/
 
 /- warning: polynomial.separable_prod_X_sub_C_iff' -> Polynomial.separable_prod_X_sub_C_iff' is a dubious translation:
-lean 3 declaration is
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {f : ι -> F} {s : Finset.{u2} ι}, Iff (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Finset.prod.{u1, u2} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.commRing.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)))) s (fun (i : ι) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (f i))))) (forall (x : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) x s) -> (forall (y : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) y s) -> (Eq.{succ u1} F (f x) (f y)) -> (Eq.{succ u2} ι x y)))
-but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} {f : ι -> F} {s : Finset.{u1} ι}, Iff (Polynomial.Separable.{u2} F (Semifield.toCommSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)) (Finset.prod.{u2, u1} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.commRing.{u2} F (EuclideanDomain.toCommRing.{u2} F (Field.toEuclideanDomain.{u2} F _inst_1)))) s (fun (i : ι) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (f i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHSub.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.sub.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (Polynomial.X.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (f i))))) (forall (x : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) x s) -> (forall (y : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) y s) -> (Eq.{succ u2} F (f x) (f y)) -> (Eq.{succ u1} ι x y)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.separable_prod_X_sub_C_iff' Polynomial.separable_prod_X_sub_C_iff'ₓ'. -/
 theorem separable_prod_X_sub_C_iff' {ι : Sort _} {f : ι → F} {s : Finset ι} :
     (∏ i in s, X - C (f i)).Separable ↔ ∀ x ∈ s, ∀ y ∈ s, f x = f y → x = y :=
@@ -445,10 +433,7 @@ theorem separable_prod_X_sub_C_iff' {ι : Sort _} {f : ι → F} {s : Finset ι}
 #align polynomial.separable_prod_X_sub_C_iff' Polynomial.separable_prod_X_sub_C_iff'
 
 /- warning: polynomial.separable_prod_X_sub_C_iff -> Polynomial.separable_prod_X_sub_C_iff is a dubious translation:
-lean 3 declaration is
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_3 : Fintype.{u2} ι] {f : ι -> F}, Iff (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Finset.prod.{u1, u2} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.commRing.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)))) (Finset.univ.{u2} ι _inst_3) (fun (i : ι) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (f i))))) (Function.Injective.{succ u2, succ u1} ι F f)
-but is expected to have type
-  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_3 : Fintype.{u1} ι] {f : ι -> F}, Iff (Polynomial.Separable.{u2} F (Semifield.toCommSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)) (Finset.prod.{u2, u1} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.commRing.{u2} F (EuclideanDomain.toCommRing.{u2} F (Field.toEuclideanDomain.{u2} F _inst_1)))) (Finset.univ.{u1} ι _inst_3) (fun (i : ι) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (f i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHSub.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.sub.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (Polynomial.X.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (f i))))) (Function.Injective.{succ u1, succ u2} ι F f)
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.separable_prod_X_sub_C_iff Polynomial.separable_prod_X_sub_C_iffₓ'. -/
 theorem separable_prod_X_sub_C_iff {ι : Sort _} [Fintype ι] {f : ι → F} :
     (∏ i, X - C (f i)).Separable ↔ Function.Injective f :=
@@ -462,10 +447,7 @@ variable (p : ℕ) [HF : CharP F p]
 include HF
 
 /- warning: polynomial.separable_or -> Polynomial.separable_or is a dubious translation:
-lean 3 declaration is
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (p : Nat) [HF : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) p] {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f) -> (Or (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) f) (And (Not (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) f)) (Exists.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (fun (g : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) => And (Irreducible.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) g) (Eq.{succ u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (fun (_x : AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) => (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) -> (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) ([anonymous].{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) p) g) f)))))
-but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (p : Nat) [HF : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (Ring.toAddGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) p] {f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) f) -> (Or (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) f) (And (Not (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) f)) (Exists.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (g : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => And (Irreducible.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) g) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) g) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AlgHom.algHomClass.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) p) g) f)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.separable_or Polynomial.separable_orₓ'. -/
 theorem separable_or {f : F[X]} (hf : Irreducible f) :
     f.Separable ∨ ¬f.Separable ∧ ∃ g : F[X], Irreducible g ∧ expand F p g = f :=
@@ -485,10 +467,7 @@ theorem separable_or {f : F[X]} (hf : Irreducible f) :
 #align polynomial.separable_or Polynomial.separable_or
 
 /- warning: polynomial.exists_separable_of_irreducible -> Polynomial.exists_separable_of_irreducible is a dubious translation:
-lean 3 declaration is
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (p : Nat) [HF : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) p] {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f) -> (Ne.{1} Nat p (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Exists.{1} Nat (fun (n : Nat) => Exists.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (fun (g : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) => And (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) g) (Eq.{succ u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (fun (_x : AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) => (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) -> (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) ([anonymous].{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) g) f))))
-but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (p : Nat) [HF : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (Ring.toAddGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) p] {f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) f) -> (Ne.{1} Nat p (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Exists.{1} Nat (fun (n : Nat) => Exists.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (g : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => And (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) g) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) g) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AlgHom.algHomClass.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) g) f))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.exists_separable_of_irreducible Polynomial.exists_separable_of_irreducibleₓ'. -/
 theorem exists_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : p ≠ 0) :
     ∃ (n : ℕ)(g : F[X]), g.Separable ∧ expand F (p ^ n) g = f :=
@@ -519,10 +498,7 @@ theorem exists_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : p
 #align polynomial.exists_separable_of_irreducible Polynomial.exists_separable_of_irreducible
 
 /- warning: polynomial.is_unit_or_eq_zero_of_separable_expand -> Polynomial.isUnit_or_eq_zero_of_separable_expand is a dubious translation:
-lean 3 declaration is
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (p : Nat) [HF : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) p] {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))} (n : Nat), (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) p) -> (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (coeFn.{succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (fun (_x : AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) => (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) -> (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) ([anonymous].{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) f)) -> (Or (IsUnit.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f) (Eq.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))))
-but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (p : Nat) [HF : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (Ring.toAddGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) p] {f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))} (n : Nat), (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) p) -> (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AlgHom.algHomClass.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) f)) -> (Or (IsUnit.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) f) (Eq.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.is_unit_or_eq_zero_of_separable_expand Polynomial.isUnit_or_eq_zero_of_separable_expandₓ'. -/
 theorem isUnit_or_eq_zero_of_separable_expand {f : F[X]} (n : ℕ) (hp : 0 < p)
     (hf : (expand F (p ^ n) f).Separable) : IsUnit f ∨ n = 0 :=
@@ -539,10 +515,7 @@ theorem isUnit_or_eq_zero_of_separable_expand {f : F[X]} (n : ℕ) (hp : 0 < p)
 #align polynomial.is_unit_or_eq_zero_of_separable_expand Polynomial.isUnit_or_eq_zero_of_separable_expand
 
 /- warning: polynomial.unique_separable_of_irreducible -> Polynomial.unique_separable_of_irreducible is a dubious translation:
-lean 3 declaration is
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (p : Nat) [HF : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) p] {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f) -> (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) p) -> (forall (n₁ : Nat) (g₁ : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))), (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) g₁) -> (Eq.{succ u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (fun (_x : AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) => (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) -> (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) ([anonymous].{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n₁)) g₁) f) -> (forall (n₂ : Nat) (g₂ : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))), (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) g₂) -> (Eq.{succ u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (fun (_x : AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) => (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) -> (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) ([anonymous].{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n₂)) g₂) f) -> (And (Eq.{1} Nat n₁ n₂) (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) g₁ g₂))))
-but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (p : Nat) [HF : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (Ring.toAddGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) p] {f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) f) -> (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) p) -> (forall (n₁ : Nat) (g₁ : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))), (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) g₁) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) g₁) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AlgHom.algHomClass.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n₁)) g₁) f) -> (forall (n₂ : Nat) (g₂ : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))), (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) g₂) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) g₂) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AlgHom.algHomClass.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n₂)) g₂) f) -> (And (Eq.{1} Nat n₁ n₂) (Eq.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) g₁ g₂))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.unique_separable_of_irreducible Polynomial.unique_separable_of_irreducibleₓ'. -/
 theorem unique_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : 0 < p) (n₁ : ℕ)
     (g₁ : F[X]) (hg₁ : g₁.Separable) (hgf₁ : expand F (p ^ n₁) g₁ = f) (n₂ : ℕ) (g₂ : F[X])
@@ -571,10 +544,7 @@ theorem unique_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : 0
 end CharP
 
 /- warning: polynomial.separable_X_pow_sub_C -> Polynomial.separable_X_pow_sub_C is a dubious translation:
-lean 3 declaration is
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {n : Nat} (a : F), (Ne.{succ u1} F ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat F (HasLiftT.mk.{1, succ u1} Nat F (CoeTCₓ.coe.{1, succ u1} Nat F (Nat.castCoe.{u1} F (AddMonoidWithOne.toNatCast.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))) n) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Ne.{succ u1} F a (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) Nat (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHPow.{u1, 0} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.X.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) n) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) a)))
-but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {n : Nat} (a : F), (Ne.{succ u1} F (Nat.cast.{u1} F (Semiring.toNatCast.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) n) (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (CommMonoidWithZero.toZero.{u1} F (CommGroupWithZero.toCommMonoidWithZero.{u1} F (Semifield.toCommGroupWithZero.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) -> (Ne.{succ u1} F a (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (CommMonoidWithZero.toZero.{u1} F (CommGroupWithZero.toCommMonoidWithZero.{u1} F (Semifield.toCommGroupWithZero.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) -> (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) a) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) Nat (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHPow.{u1, 0} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Polynomial.X.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) n) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) a)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.separable_X_pow_sub_C Polynomial.separable_X_pow_sub_Cₓ'. -/
 /-- If `n ≠ 0` in `F`, then ` X ^ n - a` is separable for any `a ≠ 0`. -/
 theorem separable_X_pow_sub_C {n : ℕ} (a : F) (hn : (n : F) ≠ 0) (ha : a ≠ 0) :
@@ -616,10 +586,7 @@ theorem card_rootSet_eq_natDegree [Algebra F K] {p : F[X]} (hsep : p.Separable)
 variable {i : F →+* K}
 
 /- warning: polynomial.eq_X_sub_C_of_separable_of_root_eq -> Polynomial.eq_X_sub_C_of_separable_of_root_eq is a dubious translation:
-lean 3 declaration is
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {K : Type.{u2}} [_inst_2 : Field.{u2} K] {i : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : F} {h : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) h) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) x h) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Polynomial.Splits.{u1, u2} F K (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)) _inst_2 i h) -> (forall (y : K), (Membership.Mem.{u2, u2} K (Multiset.{u2} K) (Multiset.hasMem.{u2} K) y (Polynomial.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Polynomial.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) i h))) -> (Eq.{succ u2} K y (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) i x))) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) h (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.leadingCoeff.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) h)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x))))
-but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {K : Type.{u2}} [_inst_2 : Field.{u2} K] {i : RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))} {x : F} {h : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))}, (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) h) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x h) (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (CommMonoidWithZero.toZero.{u1} F (CommGroupWithZero.toCommMonoidWithZero.{u1} F (Semifield.toCommGroupWithZero.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) -> (Polynomial.Splits.{u1, u2} F K (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)) _inst_2 i h) -> (forall (y : K), (Membership.mem.{u2, u2} K (Multiset.{u2} K) (Multiset.instMembershipMultiset.{u2} K) y (Polynomial.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Polynomial.map.{u1, u2} F K (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))) i h))) -> (Eq.{succ u2} K y (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))))) i x))) -> (Eq.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) h (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) h)) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) h)) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) h)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) x) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) x))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.eq_X_sub_C_of_separable_of_root_eq Polynomial.eq_X_sub_C_of_separable_of_root_eqₓ'. -/
 theorem eq_X_sub_C_of_separable_of_root_eq {x : F} {h : F[X]} (h_sep : h.Separable)
     (h_root : h.eval x = 0) (h_splits : Splits i h) (h_roots : ∀ y ∈ (h.map i).roots, y = i x) :
@@ -642,10 +609,7 @@ theorem eq_X_sub_C_of_separable_of_root_eq {x : F} {h : F[X]} (h_sep : h.Separab
 #align polynomial.eq_X_sub_C_of_separable_of_root_eq Polynomial.eq_X_sub_C_of_separable_of_root_eq
 
 /- warning: polynomial.exists_finset_of_splits -> Polynomial.exists_finset_of_splits is a dubious translation:
-lean 3 declaration is
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {K : Type.{u2}} [_inst_2 : Field.{u2} K] (i : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) f) -> (Polynomial.Splits.{u1, u2} F K (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)) _inst_2 i f) -> (Exists.{succ u2} (Finset.{u2} K) (fun (s : Finset.{u2} K) => Eq.{succ u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) i f) (HMul.hMul.{u2, u2, u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (instHMul.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.mul'.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (fun (_x : RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) => K -> (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (Polynomial.C.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) i (Polynomial.leadingCoeff.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) f))) (Finset.prod.{u2, u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) K (CommRing.toCommMonoid.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.commRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)))) s (fun (a : K) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (instHSub.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.sub.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.X.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (fun (_x : RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) => K -> (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (Polynomial.C.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) a))))))
-but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {K : Type.{u2}} [_inst_2 : Field.{u2} K] (i : RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) {f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))}, (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) f) -> (Polynomial.Splits.{u1, u2} F K (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)) _inst_2 i f) -> (Exists.{succ u2} (Finset.{u2} K) (fun (s : Finset.{u2} K) => Eq.{succ u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Polynomial.map.{u1, u2} F K (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _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 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f))) (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f))) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f))) (Polynomial.mul'.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2))))))))) (Polynomial.C.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f))) (Finset.prod.{u2, u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) K (CommRing.toCommMonoid.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Polynomial.commRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)))) s (fun (a : K) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) a) (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (instHSub.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Polynomial.sub.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.X.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} K (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} K (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))) K (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} K (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))) K (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} K (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))) K (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} K (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))))))) (Polynomial.C.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) a))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.exists_finset_of_splits Polynomial.exists_finset_of_splitsₓ'. -/
 theorem exists_finset_of_splits (i : F →+* K) {f : F[X]} (sep : Separable f) (sp : Splits i f) :
     ∃ s : Finset K, f.map i = C (i f.leadingCoeff) * s.Prod fun a : K => X - C a :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/ef95945cd48c932c9e034872bd25c3c220d9c946

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
 
 ! This file was ported from Lean 3 source module field_theory.separable
-! leanprover-community/mathlib commit 92ca63f0fb391a9ca5f22d2409a6080e786d99f7
+! leanprover-community/mathlib commit 61db041ab8e4aaf8cb5c7dc10a7d4ff261997536
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -18,6 +18,9 @@ import Mathbin.RingTheory.PowerBasis
 
 # Separable polynomials
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We define a polynomial to be separable if it is coprime with its derivative. We prove basic
 properties about separable polynomials here.
 

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

@@ -51,7 +51,7 @@ def Separable (f : R[X]) : Prop :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Iff (Polynomial.Separable.{u1} R _inst_1 f) (IsCoprime.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1) f (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) f))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Iff (Polynomial.Separable.{u1} R _inst_1 f) (IsCoprime.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1) f (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) f))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Iff (Polynomial.Separable.{u1} R _inst_1 f) (IsCoprime.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1) f (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) f))
 Case conversion may be inaccurate. Consider using '#align polynomial.separable_def Polynomial.separable_defₓ'. -/
 theorem separable_def (f : R[X]) : f.Separable ↔ IsCoprime f f.derivative :=
   Iff.rfl
@@ -61,7 +61,7 @@ theorem separable_def (f : R[X]) : f.Separable ↔ IsCoprime f f.derivative :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Iff (Polynomial.Separable.{u1} R _inst_1 f) (Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (a : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (b : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) a f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) b (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) f))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 1 (One.one.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.hasOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Iff (Polynomial.Separable.{u1} R _inst_1 f) (Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (a : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (b : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) a f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) f) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) b (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) f))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Iff (Polynomial.Separable.{u1} R _inst_1 f) (Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (a : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (b : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) a f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) f) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) b (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) f))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.separable_def' Polynomial.separable_def'ₓ'. -/
 theorem separable_def' (f : R[X]) : f.Separable ↔ ∃ a b : R[X], a * f + b * f.derivative = 1 :=
   Iff.rfl
@@ -402,7 +402,7 @@ variable {F : Type u} [Field F] {K : Type v} [Field K]
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f) -> (Iff (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) f) (Ne.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} F F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.derivative.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f) (OfNat.ofNat.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.zero.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) f) -> (Iff (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) f) (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} F F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Polynomial.derivative.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) f) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) f) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) f) (Polynomial.zero.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) f) -> (Iff (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) f) (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} F F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Polynomial.derivative.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) f) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) f) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) f) (Polynomial.zero.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.separable_iff_derivative_ne_zero Polynomial.separable_iff_derivative_ne_zeroₓ'. -/
 theorem separable_iff_derivative_ne_zero {f : F[X]} (hf : Irreducible f) :
     f.Separable ↔ f.derivative ≠ 0 :=
@@ -462,7 +462,7 @@ include HF
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (p : Nat) [HF : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) p] {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f) -> (Or (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) f) (And (Not (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) f)) (Exists.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (fun (g : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) => And (Irreducible.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) g) (Eq.{succ u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (fun (_x : AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) => (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) -> (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) ([anonymous].{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) p) g) f)))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (p : Nat) [HF : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (Ring.toAddGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) p] {f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) f) -> (Or (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) f) (And (Not (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) f)) (Exists.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (g : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => And (Irreducible.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) g) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) g) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AlgHom.algHomClass.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) p) g) f)))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (p : Nat) [HF : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (Ring.toAddGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) p] {f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) f) -> (Or (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) f) (And (Not (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) f)) (Exists.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (g : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => And (Irreducible.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) g) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) g) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AlgHom.algHomClass.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) p) g) f)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.separable_or Polynomial.separable_orₓ'. -/
 theorem separable_or {f : F[X]} (hf : Irreducible f) :
     f.Separable ∨ ¬f.Separable ∧ ∃ g : F[X], Irreducible g ∧ expand F p g = f :=
@@ -485,7 +485,7 @@ theorem separable_or {f : F[X]} (hf : Irreducible f) :
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (p : Nat) [HF : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) p] {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f) -> (Ne.{1} Nat p (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Exists.{1} Nat (fun (n : Nat) => Exists.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (fun (g : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) => And (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) g) (Eq.{succ u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (fun (_x : AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) => (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) -> (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) ([anonymous].{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) g) f))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (p : Nat) [HF : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (Ring.toAddGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) p] {f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) f) -> (Ne.{1} Nat p (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Exists.{1} Nat (fun (n : Nat) => Exists.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (g : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => And (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) g) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) g) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AlgHom.algHomClass.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) g) f))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (p : Nat) [HF : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (Ring.toAddGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) p] {f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) f) -> (Ne.{1} Nat p (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Exists.{1} Nat (fun (n : Nat) => Exists.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (g : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => And (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) g) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) g) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AlgHom.algHomClass.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) g) f))))
 Case conversion may be inaccurate. Consider using '#align polynomial.exists_separable_of_irreducible Polynomial.exists_separable_of_irreducibleₓ'. -/
 theorem exists_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : p ≠ 0) :
     ∃ (n : ℕ)(g : F[X]), g.Separable ∧ expand F (p ^ n) g = f :=
@@ -519,7 +519,7 @@ theorem exists_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : p
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (p : Nat) [HF : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) p] {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))} (n : Nat), (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) p) -> (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (coeFn.{succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (fun (_x : AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) => (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) -> (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) ([anonymous].{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) f)) -> (Or (IsUnit.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f) (Eq.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (p : Nat) [HF : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (Ring.toAddGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) p] {f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))} (n : Nat), (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) p) -> (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AlgHom.algHomClass.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) f)) -> (Or (IsUnit.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) f) (Eq.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (p : Nat) [HF : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (Ring.toAddGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) p] {f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))} (n : Nat), (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) p) -> (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AlgHom.algHomClass.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) f)) -> (Or (IsUnit.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) f) (Eq.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))
 Case conversion may be inaccurate. Consider using '#align polynomial.is_unit_or_eq_zero_of_separable_expand Polynomial.isUnit_or_eq_zero_of_separable_expandₓ'. -/
 theorem isUnit_or_eq_zero_of_separable_expand {f : F[X]} (n : ℕ) (hp : 0 < p)
     (hf : (expand F (p ^ n) f).Separable) : IsUnit f ∨ n = 0 :=
@@ -539,7 +539,7 @@ theorem isUnit_or_eq_zero_of_separable_expand {f : F[X]} (n : ℕ) (hp : 0 < p)
 lean 3 declaration is
   forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (p : Nat) [HF : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) p] {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f) -> (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) p) -> (forall (n₁ : Nat) (g₁ : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))), (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) g₁) -> (Eq.{succ u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (fun (_x : AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) => (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) -> (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) ([anonymous].{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n₁)) g₁) f) -> (forall (n₂ : Nat) (g₂ : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))), (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) g₂) -> (Eq.{succ u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (fun (_x : AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) => (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) -> (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) ([anonymous].{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n₂)) g₂) f) -> (And (Eq.{1} Nat n₁ n₂) (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) g₁ g₂))))
 but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (p : Nat) [HF : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (Ring.toAddGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) p] {f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) f) -> (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) p) -> (forall (n₁ : Nat) (g₁ : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))), (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) g₁) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) g₁) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AlgHom.algHomClass.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n₁)) g₁) f) -> (forall (n₂ : Nat) (g₂ : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))), (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) g₂) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) g₂) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AlgHom.algHomClass.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n₂)) g₂) f) -> (And (Eq.{1} Nat n₁ n₂) (Eq.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) g₁ g₂))))
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (p : Nat) [HF : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (Ring.toAddGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) p] {f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) f) -> (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) p) -> (forall (n₁ : Nat) (g₁ : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))), (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) g₁) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) g₁) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AlgHom.algHomClass.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n₁)) g₁) f) -> (forall (n₂ : Nat) (g₂ : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))), (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) g₂) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) g₂) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AlgHom.algHomClass.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n₂)) g₂) f) -> (And (Eq.{1} Nat n₁ n₂) (Eq.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) g₁ g₂))))
 Case conversion may be inaccurate. Consider using '#align polynomial.unique_separable_of_irreducible Polynomial.unique_separable_of_irreducibleₓ'. -/
 theorem unique_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : 0 < p) (n₁ : ℕ)
     (g₁ : F[X]) (hg₁ : g₁.Separable) (hgf₁ : expand F (p ^ n₁) g₁ = f) (n₂ : ℕ) (g₂ : F[X])

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

@@ -40,83 +40,138 @@ section CommSemiring
 
 variable {R : Type u} [CommSemiring R] {S : Type v} [CommSemiring S]
 
+#print Polynomial.Separable /-
 /-- A polynomial is separable iff it is coprime with its derivative. -/
 def Separable (f : R[X]) : Prop :=
   IsCoprime f f.derivative
 #align polynomial.separable Polynomial.Separable
+-/
 
+/- warning: polynomial.separable_def -> Polynomial.separable_def is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Iff (Polynomial.Separable.{u1} R _inst_1 f) (IsCoprime.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1) f (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) f))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Iff (Polynomial.Separable.{u1} R _inst_1 f) (IsCoprime.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1) f (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) f))
+Case conversion may be inaccurate. Consider using '#align polynomial.separable_def Polynomial.separable_defₓ'. -/
 theorem separable_def (f : R[X]) : f.Separable ↔ IsCoprime f f.derivative :=
   Iff.rfl
 #align polynomial.separable_def Polynomial.separable_def
 
+/- warning: polynomial.separable_def' -> Polynomial.separable_def' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Iff (Polynomial.Separable.{u1} R _inst_1 f) (Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (a : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (b : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) a f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) b (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) f))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 1 (One.one.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.hasOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Iff (Polynomial.Separable.{u1} R _inst_1 f) (Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (a : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (b : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) a f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) f) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) b (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.derivative.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) f))) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.separable_def' Polynomial.separable_def'ₓ'. -/
 theorem separable_def' (f : R[X]) : f.Separable ↔ ∃ a b : R[X], a * f + b * f.derivative = 1 :=
   Iff.rfl
 #align polynomial.separable_def' Polynomial.separable_def'
 
+#print Polynomial.not_separable_zero /-
 theorem not_separable_zero [Nontrivial R] : ¬Separable (0 : R[X]) :=
   by
   rintro ⟨x, y, h⟩
   simpa only [derivative_zero, MulZeroClass.mul_zero, add_zero, zero_ne_one] using h
 #align polynomial.not_separable_zero Polynomial.not_separable_zero
+-/
 
+#print Polynomial.separable_one /-
 theorem separable_one : (1 : R[X]).Separable :=
   isCoprime_one_left
 #align polynomial.separable_one Polynomial.separable_one
+-/
 
+#print Polynomial.separable_of_subsingleton /-
 @[nontriviality]
 theorem separable_of_subsingleton [Subsingleton R] (f : R[X]) : f.Separable := by simp [separable]
 #align polynomial.separable_of_subsingleton Polynomial.separable_of_subsingleton
+-/
 
-theorem separable_x_add_c (a : R) : (X + C a).Separable :=
+/- warning: polynomial.separable_X_add_C -> Polynomial.separable_X_add_C is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (a : R), Polynomial.Separable.{u1} R _inst_1 (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (a : R), Polynomial.Separable.{u1} R _inst_1 (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHAdd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.add'.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a))
+Case conversion may be inaccurate. Consider using '#align polynomial.separable_X_add_C Polynomial.separable_X_add_Cₓ'. -/
+theorem separable_X_add_C (a : R) : (X + C a).Separable :=
   by
   rw [separable_def, derivative_add, derivative_X, derivative_C, add_zero]
   exact isCoprime_one_right
-#align polynomial.separable_X_add_C Polynomial.separable_x_add_c
+#align polynomial.separable_X_add_C Polynomial.separable_X_add_C
 
-theorem separable_x : (X : R[X]).Separable :=
+#print Polynomial.separable_X /-
+theorem separable_X : (X : R[X]).Separable :=
   by
   rw [separable_def, derivative_X]
   exact isCoprime_one_right
-#align polynomial.separable_X Polynomial.separable_x
+#align polynomial.separable_X Polynomial.separable_X
+-/
 
-theorem separable_c (r : R) : (C r).Separable ↔ IsUnit r := by
+/- warning: polynomial.separable_C -> Polynomial.separable_C is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (r : R), Iff (Polynomial.Separable.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => R -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) r)) (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) r)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (r : R), Iff (Polynomial.Separable.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) r)) (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) r)
+Case conversion may be inaccurate. Consider using '#align polynomial.separable_C Polynomial.separable_Cₓ'. -/
+theorem separable_C (r : R) : (C r).Separable ↔ IsUnit r := by
   rw [separable_def, derivative_C, isCoprime_zero_right, is_unit_C]
-#align polynomial.separable_C Polynomial.separable_c
+#align polynomial.separable_C Polynomial.separable_C
 
+#print Polynomial.Separable.of_mul_left /-
 theorem Separable.of_mul_left {f g : R[X]} (h : (f * g).Separable) : f.Separable :=
   by
   have := h.of_mul_left_left; rw [derivative_mul] at this
   exact IsCoprime.of_mul_right_left (IsCoprime.of_add_mul_left_right this)
 #align polynomial.separable.of_mul_left Polynomial.Separable.of_mul_left
+-/
 
+#print Polynomial.Separable.of_mul_right /-
 theorem Separable.of_mul_right {f g : R[X]} (h : (f * g).Separable) : g.Separable :=
   by
   rw [mul_comm] at h
   exact h.of_mul_left
 #align polynomial.separable.of_mul_right Polynomial.Separable.of_mul_right
+-/
 
+#print Polynomial.Separable.of_dvd /-
 theorem Separable.of_dvd {f g : R[X]} (hf : f.Separable) (hfg : g ∣ f) : g.Separable :=
   by
   rcases hfg with ⟨f', rfl⟩
   exact separable.of_mul_left hf
 #align polynomial.separable.of_dvd Polynomial.Separable.of_dvd
+-/
 
+/- warning: polynomial.separable_gcd_left -> Polynomial.separable_gcd_left is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_3 : Field.{u1} F] {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_3)))}, (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) f) -> (forall (g : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_3)))), Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (EuclideanDomain.gcd.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_3)))) (Polynomial.euclideanDomain.{u1} F _inst_3) (fun (a : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_3)))) (b : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_3)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_3)))) a b)) f g))
+but is expected to have type
+  forall {F : Type.{u1}} [_inst_3 : Field.{u1} F] {f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)))}, (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) f) -> (forall (g : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)))), Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (EuclideanDomain.gcd.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_3) (fun (a : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)))) (b : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)))) a b)) f g))
+Case conversion may be inaccurate. Consider using '#align polynomial.separable_gcd_left Polynomial.separable_gcd_leftₓ'. -/
 theorem separable_gcd_left {F : Type _} [Field F] {f : F[X]} (hf : f.Separable) (g : F[X]) :
     (EuclideanDomain.gcd f g).Separable :=
   Separable.of_dvd hf (EuclideanDomain.gcd_dvd_left f g)
 #align polynomial.separable_gcd_left Polynomial.separable_gcd_left
 
+/- warning: polynomial.separable_gcd_right -> Polynomial.separable_gcd_right is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_3 : Field.{u1} F] {g : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_3)))} (f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_3)))), (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) g) -> (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (EuclideanDomain.gcd.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_3)))) (Polynomial.euclideanDomain.{u1} F _inst_3) (fun (a : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_3)))) (b : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_3)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_3)))) a b)) f g))
+but is expected to have type
+  forall {F : Type.{u1}} [_inst_3 : Field.{u1} F] {g : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)))} (f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)))), (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) g) -> (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)) (EuclideanDomain.gcd.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)))) (Polynomial.instEuclideanDomainPolynomialToSemiringToDivisionSemiringToSemifield.{u1} F _inst_3) (fun (a : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)))) (b : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)))) => Classical.propDecidable (Eq.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_3)))) a b)) f g))
+Case conversion may be inaccurate. Consider using '#align polynomial.separable_gcd_right Polynomial.separable_gcd_rightₓ'. -/
 theorem separable_gcd_right {F : Type _} [Field F] {g : F[X]} (f : F[X]) (hg : g.Separable) :
     (EuclideanDomain.gcd f g).Separable :=
   Separable.of_dvd hg (EuclideanDomain.gcd_dvd_right f g)
 #align polynomial.separable_gcd_right Polynomial.separable_gcd_right
 
+#print Polynomial.Separable.isCoprime /-
 theorem Separable.isCoprime {f g : R[X]} (h : (f * g).Separable) : IsCoprime f g :=
   by
   have := h.of_mul_left_left; rw [derivative_mul] at this
   exact IsCoprime.of_mul_right_right (IsCoprime.of_add_mul_left_right this)
 #align polynomial.separable.is_coprime Polynomial.Separable.isCoprime
+-/
 
+#print Polynomial.Separable.of_pow' /-
 theorem Separable.of_pow' {f : R[X]} :
     ∀ {n : ℕ} (h : (f ^ n).Separable), IsUnit f ∨ f.Separable ∧ n = 1 ∨ n = 0
   | 0 => fun h => Or.inr <| Or.inr rfl
@@ -125,21 +180,27 @@ theorem Separable.of_pow' {f : R[X]} :
     rw [pow_succ, pow_succ] at h
     exact Or.inl (isCoprime_self.1 h.is_coprime.of_mul_right_left)
 #align polynomial.separable.of_pow' Polynomial.Separable.of_pow'
+-/
 
+#print Polynomial.Separable.of_pow /-
 theorem Separable.of_pow {f : R[X]} (hf : ¬IsUnit f) {n : ℕ} (hn : n ≠ 0)
     (hfs : (f ^ n).Separable) : f.Separable ∧ n = 1 :=
   (hfs.of_pow'.resolve_left hf).resolve_right hn
 #align polynomial.separable.of_pow Polynomial.Separable.of_pow
+-/
 
+#print Polynomial.Separable.map /-
 theorem Separable.map {p : R[X]} (h : p.Separable) {f : R →+* S} : (p.map f).Separable :=
   let ⟨a, b, H⟩ := h
   ⟨a.map f, b.map f, by
     rw [derivative_map, ← Polynomial.map_mul, ← Polynomial.map_mul, ← Polynomial.map_add, H,
       Polynomial.map_one]⟩
 #align polynomial.separable.map Polynomial.Separable.map
+-/
 
 variable (p q : ℕ)
 
+#print Polynomial.isUnit_of_self_mul_dvd_separable /-
 theorem isUnit_of_self_mul_dvd_separable {p q : R[X]} (hp : p.Separable) (hq : q * q ∣ p) :
     IsUnit q := by
   obtain ⟨p, rfl⟩ := hq
@@ -152,7 +213,9 @@ theorem isUnit_of_self_mul_dvd_separable {p q : R[X]} (hp : p.Separable) (hq : q
     ring
   exact IsCoprime.of_mul_right_left (IsCoprime.of_mul_left_left this)
 #align polynomial.is_unit_of_self_mul_dvd_separable Polynomial.isUnit_of_self_mul_dvd_separable
+-/
 
+#print Polynomial.multiplicity_le_one_of_separable /-
 theorem multiplicity_le_one_of_separable {p q : R[X]} (hq : ¬IsUnit q) (hsep : Separable p) :
     multiplicity q p ≤ 1 := by
   contrapose! hq
@@ -161,7 +224,9 @@ theorem multiplicity_le_one_of_separable {p q : R[X]} (hq : ¬IsUnit q) (hsep :
   apply multiplicity.pow_dvd_of_le_multiplicity
   simpa only [Nat.cast_one, Nat.cast_bit0] using PartENat.add_one_le_of_lt hq
 #align polynomial.multiplicity_le_one_of_separable Polynomial.multiplicity_le_one_of_separable
+-/
 
+#print Polynomial.Separable.squarefree /-
 theorem Separable.squarefree {p : R[X]} (hsep : Separable p) : Squarefree p :=
   by
   rw [multiplicity.squarefree_iff_multiplicity_le_one p]
@@ -170,6 +235,7 @@ theorem Separable.squarefree {p : R[X]} (hsep : Separable p) : Squarefree p :=
   · exact Or.inr hunit
   exact Or.inl (multiplicity_le_one_of_separable hunit hsep)
 #align polynomial.separable.squarefree Polynomial.Separable.squarefree
+-/
 
 end CommSemiring
 
@@ -177,17 +243,31 @@ section CommRing
 
 variable {R : Type u} [CommRing R]
 
-theorem separable_x_sub_c {x : R} : Separable (X - C x) := by
+/- warning: polynomial.separable_X_sub_C -> Polynomial.separable_X_sub_C is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R}, Polynomial.Separable.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) x))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R}, Polynomial.Separable.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) x) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) x))
+Case conversion may be inaccurate. Consider using '#align polynomial.separable_X_sub_C Polynomial.separable_X_sub_Cₓ'. -/
+theorem separable_X_sub_C {x : R} : Separable (X - C x) := by
   simpa only [sub_eq_add_neg, C_neg] using separable_X_add_C (-x)
-#align polynomial.separable_X_sub_C Polynomial.separable_x_sub_c
+#align polynomial.separable_X_sub_C Polynomial.separable_X_sub_C
 
+#print Polynomial.Separable.mul /-
 theorem Separable.mul {f g : R[X]} (hf : f.Separable) (hg : g.Separable) (h : IsCoprime f g) :
     (f * g).Separable := by
   rw [separable_def, derivative_mul]
   exact
     ((hf.mul_right h).add_mul_left_right _).mul_left ((h.symm.mul_right hg).mul_add_right_right _)
 #align polynomial.separable.mul Polynomial.Separable.mul
+-/
 
+/- warning: polynomial.separable_prod' -> Polynomial.separable_prod' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {ι : Type.{u2}} {f : ι -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))} {s : Finset.{u2} ι}, (forall (x : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) x s) -> (forall (y : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) y s) -> (Ne.{succ u2} ι x y) -> (IsCoprime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (f x) (f y)))) -> (forall (x : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) x s) -> (Polynomial.Separable.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (f x))) -> (Polynomial.Separable.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Finset.prod.{u1, u2} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) s (fun (x : ι) => f x)))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {ι : Type.{u1}} {f : ι -> (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))} {s : Finset.{u1} ι}, (forall (x : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) x s) -> (forall (y : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) y s) -> (Ne.{succ u1} ι x y) -> (IsCoprime.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.commSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (f x) (f y)))) -> (forall (x : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) x s) -> (Polynomial.Separable.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1) (f x))) -> (Polynomial.Separable.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1) (Finset.prod.{u2, u1} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.commRing.{u2} R _inst_1)) s (fun (x : ι) => f x)))
+Case conversion may be inaccurate. Consider using '#align polynomial.separable_prod' Polynomial.separable_prod'ₓ'. -/
 theorem separable_prod' {ι : Sort _} {f : ι → R[X]} {s : Finset ι} :
     (∀ x ∈ s, ∀ y ∈ s, x ≠ y → IsCoprime (f x) (f y)) →
       (∀ x ∈ s, (f x).Separable) → (∏ x in s, f x).Separable :=
@@ -199,12 +279,24 @@ theorem separable_prod' {ι : Sort _} {f : ι → R[X]} {s : Finset ι} :
         (IsCoprime.prod_right fun i his => h1.1.2 i his <| Ne.symm <| ne_of_mem_of_not_mem his has)
 #align polynomial.separable_prod' Polynomial.separable_prod'
 
+/- warning: polynomial.separable_prod -> Polynomial.separable_prod is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {ι : Type.{u2}} [_inst_2 : Fintype.{u2} ι] {f : ι -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))}, (Pairwise.{u2} ι (Function.onFun.{succ u2, succ u1, 1} ι (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Prop (IsCoprime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) f)) -> (forall (x : ι), Polynomial.Separable.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (f x)) -> (Polynomial.Separable.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Finset.prod.{u1, u2} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Finset.univ.{u2} ι _inst_2) (fun (x : ι) => f x)))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {ι : Type.{u1}} [_inst_2 : Fintype.{u1} ι] {f : ι -> (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))}, (Pairwise.{u1} ι (Function.onFun.{succ u1, succ u2, 1} ι (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Prop (IsCoprime.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.commSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) f)) -> (forall (x : ι), Polynomial.Separable.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1) (f x)) -> (Polynomial.Separable.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1) (Finset.prod.{u2, u1} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.commRing.{u2} R _inst_1)) (Finset.univ.{u1} ι _inst_2) (fun (x : ι) => f x)))
+Case conversion may be inaccurate. Consider using '#align polynomial.separable_prod Polynomial.separable_prodₓ'. -/
 theorem separable_prod {ι : Sort _} [Fintype ι] {f : ι → R[X]} (h1 : Pairwise (IsCoprime on f))
     (h2 : ∀ x, (f x).Separable) : (∏ x, f x).Separable :=
   separable_prod' (fun x hx y hy hxy => h1 hxy) fun x hx => h2 x
 #align polynomial.separable_prod Polynomial.separable_prod
 
-theorem Separable.inj_of_prod_x_sub_c [Nontrivial R] {ι : Sort _} {f : ι → R} {s : Finset ι}
+/- warning: polynomial.separable.inj_of_prod_X_sub_C -> Polynomial.Separable.inj_of_prod_X_sub_C is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] {ι : Type.{u2}} {f : ι -> R} {s : Finset.{u2} ι}, (Polynomial.Separable.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Finset.prod.{u1, u2} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) s (fun (i : ι) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (f i))))) -> (forall {x : ι} {y : ι}, (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) x s) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) y s) -> (Eq.{succ u1} R (f x) (f y)) -> (Eq.{succ u2} ι x y))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] [_inst_2 : Nontrivial.{u2} R] {ι : Type.{u1}} {f : ι -> R} {s : Finset.{u1} ι}, (Polynomial.Separable.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1) (Finset.prod.{u2, u1} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.commRing.{u2} R _inst_1)) s (fun (i : ι) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (f i)) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (instHSub.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.sub.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Polynomial.X.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Polynomial.C.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (f i))))) -> (forall {x : ι} {y : ι}, (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) x s) -> (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) y s) -> (Eq.{succ u2} R (f x) (f y)) -> (Eq.{succ u1} ι x y))
+Case conversion may be inaccurate. Consider using '#align polynomial.separable.inj_of_prod_X_sub_C Polynomial.Separable.inj_of_prod_X_sub_Cₓ'. -/
+theorem Separable.inj_of_prod_X_sub_C [Nontrivial R] {ι : Sort _} {f : ι → R} {s : Finset ι}
     (hfs : (∏ i in s, X - C (f i)).Separable) {x y : ι} (hx : x ∈ s) (hy : y ∈ s)
     (hfxy : f x = f y) : x = y := by
   by_contra hxy
@@ -212,13 +304,25 @@ theorem Separable.inj_of_prod_x_sub_c [Nontrivial R] {ι : Sort _} {f : ι → R
     insert_erase (mem_erase_of_ne_of_mem (Ne.symm hxy) hy), prod_insert (not_mem_erase _ _), ←
     mul_assoc, hfxy, ← sq] at hfs
   cases (hfs.of_mul_left.of_pow (not_is_unit_X_sub_C _) two_ne_zero).2
-#align polynomial.separable.inj_of_prod_X_sub_C Polynomial.Separable.inj_of_prod_x_sub_c
-
-theorem Separable.injective_of_prod_x_sub_c [Nontrivial R] {ι : Sort _} [Fintype ι] {f : ι → R}
+#align polynomial.separable.inj_of_prod_X_sub_C Polynomial.Separable.inj_of_prod_X_sub_C
+
+/- warning: polynomial.separable.injective_of_prod_X_sub_C -> Polynomial.Separable.injective_of_prod_X_sub_C is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] {ι : Type.{u2}} [_inst_3 : Fintype.{u2} ι] {f : ι -> R}, (Polynomial.Separable.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Finset.prod.{u1, u2} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Finset.univ.{u2} ι _inst_3) (fun (i : ι) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (f i))))) -> (Function.Injective.{succ u2, succ u1} ι R f)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] [_inst_2 : Nontrivial.{u2} R] {ι : Type.{u1}} [_inst_3 : Fintype.{u1} ι] {f : ι -> R}, (Polynomial.Separable.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1) (Finset.prod.{u2, u1} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.commRing.{u2} R _inst_1)) (Finset.univ.{u1} ι _inst_3) (fun (i : ι) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (f i)) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (instHSub.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.sub.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Polynomial.X.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Polynomial.C.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (f i))))) -> (Function.Injective.{succ u1, succ u2} ι R f)
+Case conversion may be inaccurate. Consider using '#align polynomial.separable.injective_of_prod_X_sub_C Polynomial.Separable.injective_of_prod_X_sub_Cₓ'. -/
+theorem Separable.injective_of_prod_X_sub_C [Nontrivial R] {ι : Sort _} [Fintype ι] {f : ι → R}
     (hfs : (∏ i, X - C (f i)).Separable) : Function.Injective f := fun x y hfxy =>
-  hfs.inj_of_prod_x_sub_c (mem_univ _) (mem_univ _) hfxy
-#align polynomial.separable.injective_of_prod_X_sub_C Polynomial.Separable.injective_of_prod_x_sub_c
-
+  hfs.inj_of_prod_X_sub_C (mem_univ _) (mem_univ _) hfxy
+#align polynomial.separable.injective_of_prod_X_sub_C Polynomial.Separable.injective_of_prod_X_sub_C
+
+/- warning: polynomial.nodup_of_separable_prod -> Polynomial.nodup_of_separable_prod is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] {s : Multiset.{u1} R}, (Polynomial.Separable.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a)) s))) -> (Multiset.Nodup.{u1} R s)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] {s : Multiset.{u1} R}, (Polynomial.Separable.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Multiset.prod.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1)) (Multiset.map.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (a : R) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a)) s))) -> (Multiset.Nodup.{u1} R s)
+Case conversion may be inaccurate. Consider using '#align polynomial.nodup_of_separable_prod Polynomial.nodup_of_separable_prodₓ'. -/
 theorem nodup_of_separable_prod [Nontrivial R] {s : Multiset R}
     (hs : Separable (Multiset.map (fun a => X - C a) s).Prod) : s.Nodup :=
   by
@@ -228,8 +332,14 @@ theorem nodup_of_separable_prod [Nontrivial R] {s : Multiset R}
   simpa only [Multiset.map_cons, Multiset.prod_cons] using mul_dvd_mul_left _ (dvd_mul_right _ _)
 #align polynomial.nodup_of_separable_prod Polynomial.nodup_of_separable_prod
 
+/- warning: polynomial.separable_X_pow_sub_C_unit -> Polynomial.separable_X_pow_sub_C_unit is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {n : Nat} (u : Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1))), (IsUnit.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) n)) -> (Polynomial.Separable.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (coeBase.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Units.hasCoe.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) u))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {n : Nat} (u : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))), (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n)) -> (Polynomial.Separable.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) u)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) n) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) u))))
+Case conversion may be inaccurate. Consider using '#align polynomial.separable_X_pow_sub_C_unit Polynomial.separable_X_pow_sub_C_unitₓ'. -/
 /-- If `is_unit n` in a `comm_ring R`, then `X ^ n - u` is separable for any unit `u`. -/
-theorem separable_x_pow_sub_c_unit {n : ℕ} (u : Rˣ) (hn : IsUnit (n : R)) :
+theorem separable_X_pow_sub_C_unit {n : ℕ} (u : Rˣ) (hn : IsUnit (n : R)) :
     Separable (X ^ n - C (u : R)) := by
   nontriviality R
   rcases n.eq_zero_or_pos with (rfl | hpos)
@@ -248,8 +358,9 @@ theorem separable_x_pow_sub_c_unit {n : ℕ} (u : Rˣ) (hn : IsUnit (n : R)) :
       simp only [Units.inv_mul, hn', C.map_one, mul_one, ← pow_succ,
         Nat.sub_add_cancel (show 1 ≤ n from hpos), sub_add_cancel]
     
-#align polynomial.separable_X_pow_sub_C_unit Polynomial.separable_x_pow_sub_c_unit
+#align polynomial.separable_X_pow_sub_C_unit Polynomial.separable_X_pow_sub_C_unit
 
+#print Polynomial.rootMultiplicity_le_one_of_separable /-
 theorem rootMultiplicity_le_one_of_separable [Nontrivial R] {p : R[X]} (hsep : Separable p)
     (x : R) : rootMultiplicity x p ≤ 1 :=
   by
@@ -259,6 +370,7 @@ theorem rootMultiplicity_le_one_of_separable [Nontrivial R] {p : R[X]} (hsep : S
     Nat.cast_one]
   exact multiplicity_le_one_of_separable (not_is_unit_X_sub_C _) hsep
 #align polynomial.root_multiplicity_le_one_of_separable Polynomial.rootMultiplicity_le_one_of_separable
+-/
 
 end CommRing
 
@@ -266,15 +378,19 @@ section IsDomain
 
 variable {R : Type u} [CommRing R] [IsDomain R]
 
+#print Polynomial.count_roots_le_one /-
 theorem count_roots_le_one {p : R[X]} (hsep : Separable p) (x : R) : p.roots.count x ≤ 1 :=
   by
   rw [count_roots p]
   exact root_multiplicity_le_one_of_separable hsep x
 #align polynomial.count_roots_le_one Polynomial.count_roots_le_one
+-/
 
+#print Polynomial.nodup_roots /-
 theorem nodup_roots {p : R[X]} (hsep : Separable p) : p.roots.Nodup :=
   Multiset.nodup_iff_count_le_one.mpr (count_roots_le_one hsep)
 #align polynomial.nodup_roots Polynomial.nodup_roots
+-/
 
 end IsDomain
 
@@ -282,6 +398,12 @@ section Field
 
 variable {F : Type u} [Field F] {K : Type v} [Field K]
 
+/- warning: polynomial.separable_iff_derivative_ne_zero -> Polynomial.separable_iff_derivative_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f) -> (Iff (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) f) (Ne.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : LinearMap.{u1, u1, u1, u1} F F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} F F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Semiring.toModule.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.derivative.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f) (OfNat.ofNat.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.zero.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))))
+but is expected to have type
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) f) -> (Iff (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) f) (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} F F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} F F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.module.{u1, u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Semiring.toModule.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.id.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Polynomial.derivative.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) f) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) f) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) f) (Polynomial.zero.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.separable_iff_derivative_ne_zero Polynomial.separable_iff_derivative_ne_zeroₓ'. -/
 theorem separable_iff_derivative_ne_zero {f : F[X]} (hf : Irreducible f) :
     f.Separable ↔ f.derivative ≠ 0 :=
   ⟨fun h1 h2 => hf.not_unit <| isCoprime_zero_right.1 <| h2 ▸ h1, fun h =>
@@ -294,13 +416,21 @@ theorem separable_iff_derivative_ne_zero {f : F[X]} (hf : Irreducible f) :
         natDegree_derivative_lt <| mt derivative_of_natDegree_zero h⟩
 #align polynomial.separable_iff_derivative_ne_zero Polynomial.separable_iff_derivative_ne_zero
 
+#print Polynomial.separable_map /-
 theorem separable_map (f : F →+* K) {p : F[X]} : (p.map f).Separable ↔ p.Separable := by
   simp_rw [separable_def, derivative_map, is_coprime_map]
 #align polynomial.separable_map Polynomial.separable_map
+-/
 
-theorem separable_prod_x_sub_c_iff' {ι : Sort _} {f : ι → F} {s : Finset ι} :
+/- warning: polynomial.separable_prod_X_sub_C_iff' -> Polynomial.separable_prod_X_sub_C_iff' is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} {f : ι -> F} {s : Finset.{u2} ι}, Iff (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Finset.prod.{u1, u2} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.commRing.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)))) s (fun (i : ι) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (f i))))) (forall (x : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) x s) -> (forall (y : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) y s) -> (Eq.{succ u1} F (f x) (f y)) -> (Eq.{succ u2} ι x y)))
+but is expected to have type
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} {f : ι -> F} {s : Finset.{u1} ι}, Iff (Polynomial.Separable.{u2} F (Semifield.toCommSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)) (Finset.prod.{u2, u1} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.commRing.{u2} F (EuclideanDomain.toCommRing.{u2} F (Field.toEuclideanDomain.{u2} F _inst_1)))) s (fun (i : ι) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (f i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHSub.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.sub.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (Polynomial.X.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (f i))))) (forall (x : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) x s) -> (forall (y : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) y s) -> (Eq.{succ u2} F (f x) (f y)) -> (Eq.{succ u1} ι x y)))
+Case conversion may be inaccurate. Consider using '#align polynomial.separable_prod_X_sub_C_iff' Polynomial.separable_prod_X_sub_C_iff'ₓ'. -/
+theorem separable_prod_X_sub_C_iff' {ι : Sort _} {f : ι → F} {s : Finset ι} :
     (∏ i in s, X - C (f i)).Separable ↔ ∀ x ∈ s, ∀ y ∈ s, f x = f y → x = y :=
-  ⟨fun hfs x hx y hy hfxy => hfs.inj_of_prod_x_sub_c hx hy hfxy, fun H =>
+  ⟨fun hfs x hx y hy hfxy => hfs.inj_of_prod_X_sub_C hx hy hfxy, fun H =>
     by
     rw [← prod_attach]
     exact
@@ -309,12 +439,18 @@ theorem separable_prod_x_sub_c_iff' {ι : Sort _} {f : ι → F} {s : Finset ι}
           @pairwise_coprime_X_sub_C _ _ { x // x ∈ s } (fun x => f x)
             (fun x y hxy => Subtype.eq <| H x.1 x.2 y.1 y.2 hxy) _ _ hxy)
         fun _ _ => separable_X_sub_C⟩
-#align polynomial.separable_prod_X_sub_C_iff' Polynomial.separable_prod_x_sub_c_iff'
-
-theorem separable_prod_x_sub_c_iff {ι : Sort _} [Fintype ι] {f : ι → F} :
+#align polynomial.separable_prod_X_sub_C_iff' Polynomial.separable_prod_X_sub_C_iff'
+
+/- warning: polynomial.separable_prod_X_sub_C_iff -> Polynomial.separable_prod_X_sub_C_iff is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {ι : Type.{u2}} [_inst_3 : Fintype.{u2} ι] {f : ι -> F}, Iff (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Finset.prod.{u1, u2} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) ι (CommRing.toCommMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.commRing.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)))) (Finset.univ.{u2} ι _inst_3) (fun (i : ι) => HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (f i))))) (Function.Injective.{succ u2, succ u1} ι F f)
+but is expected to have type
+  forall {F : Type.{u2}} [_inst_1 : Field.{u2} F] {ι : Type.{u1}} [_inst_3 : Fintype.{u1} ι] {f : ι -> F}, Iff (Polynomial.Separable.{u2} F (Semifield.toCommSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)) (Finset.prod.{u2, u1} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ι (CommRing.toCommMonoid.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.commRing.{u2} F (EuclideanDomain.toCommRing.{u2} F (Field.toEuclideanDomain.{u2} F _inst_1)))) (Finset.univ.{u1} ι _inst_3) (fun (i : ι) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (f i)) (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (instHSub.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.sub.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (Polynomial.X.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u2, u2} F (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Polynomial.semiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))))))) (Polynomial.C.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (f i))))) (Function.Injective.{succ u1, succ u2} ι F f)
+Case conversion may be inaccurate. Consider using '#align polynomial.separable_prod_X_sub_C_iff Polynomial.separable_prod_X_sub_C_iffₓ'. -/
+theorem separable_prod_X_sub_C_iff {ι : Sort _} [Fintype ι] {f : ι → F} :
     (∏ i, X - C (f i)).Separable ↔ Function.Injective f :=
-  separable_prod_x_sub_c_iff'.trans <| by simp_rw [mem_univ, true_imp_iff, Function.Injective]
-#align polynomial.separable_prod_X_sub_C_iff Polynomial.separable_prod_x_sub_c_iff
+  separable_prod_X_sub_C_iff'.trans <| by simp_rw [mem_univ, true_imp_iff, Function.Injective]
+#align polynomial.separable_prod_X_sub_C_iff Polynomial.separable_prod_X_sub_C_iff
 
 section CharP
 
@@ -322,6 +458,12 @@ variable (p : ℕ) [HF : CharP F p]
 
 include HF
 
+/- warning: polynomial.separable_or -> Polynomial.separable_or is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (p : Nat) [HF : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) p] {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f) -> (Or (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) f) (And (Not (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) f)) (Exists.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (fun (g : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) => And (Irreducible.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) g) (Eq.{succ u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (fun (_x : AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) => (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) -> (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) ([anonymous].{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) p) g) f)))))
+but is expected to have type
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (p : Nat) [HF : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (Ring.toAddGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) p] {f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) f) -> (Or (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) f) (And (Not (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) f)) (Exists.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (g : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => And (Irreducible.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) g) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) g) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AlgHom.algHomClass.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) p) g) f)))))
+Case conversion may be inaccurate. Consider using '#align polynomial.separable_or Polynomial.separable_orₓ'. -/
 theorem separable_or {f : F[X]} (hf : Irreducible f) :
     f.Separable ∨ ¬f.Separable ∧ ∃ g : F[X], Irreducible g ∧ expand F p g = f :=
   if H : f.derivative = 0 then by
@@ -339,6 +481,12 @@ theorem separable_or {f : F[X]} (hf : Irreducible f) :
   else Or.inl <| (separable_iff_derivative_ne_zero hf).2 H
 #align polynomial.separable_or Polynomial.separable_or
 
+/- warning: polynomial.exists_separable_of_irreducible -> Polynomial.exists_separable_of_irreducible is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (p : Nat) [HF : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) p] {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f) -> (Ne.{1} Nat p (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Exists.{1} Nat (fun (n : Nat) => Exists.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (fun (g : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) => And (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) g) (Eq.{succ u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (fun (_x : AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) => (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) -> (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) ([anonymous].{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) g) f))))
+but is expected to have type
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (p : Nat) [HF : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (Ring.toAddGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) p] {f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) f) -> (Ne.{1} Nat p (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Exists.{1} Nat (fun (n : Nat) => Exists.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (g : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => And (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) g) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) g) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AlgHom.algHomClass.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) g) f))))
+Case conversion may be inaccurate. Consider using '#align polynomial.exists_separable_of_irreducible Polynomial.exists_separable_of_irreducibleₓ'. -/
 theorem exists_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : p ≠ 0) :
     ∃ (n : ℕ)(g : F[X]), g.Separable ∧ expand F (p ^ n) g = f :=
   by
@@ -367,6 +515,12 @@ theorem exists_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : p
     rw [← hgf, expand_expand, pow_succ]
 #align polynomial.exists_separable_of_irreducible Polynomial.exists_separable_of_irreducible
 
+/- warning: polynomial.is_unit_or_eq_zero_of_separable_expand -> Polynomial.isUnit_or_eq_zero_of_separable_expand is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (p : Nat) [HF : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) p] {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))} (n : Nat), (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) p) -> (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (coeFn.{succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (fun (_x : AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) => (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) -> (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) ([anonymous].{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n)) f)) -> (Or (IsUnit.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f) (Eq.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))))
+but is expected to have type
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (p : Nat) [HF : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (Ring.toAddGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) p] {f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))} (n : Nat), (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) p) -> (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AlgHom.algHomClass.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n)) f)) -> (Or (IsUnit.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) f) (Eq.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))
+Case conversion may be inaccurate. Consider using '#align polynomial.is_unit_or_eq_zero_of_separable_expand Polynomial.isUnit_or_eq_zero_of_separable_expandₓ'. -/
 theorem isUnit_or_eq_zero_of_separable_expand {f : F[X]} (n : ℕ) (hp : 0 < p)
     (hf : (expand F (p ^ n) f).Separable) : IsUnit f ∨ n = 0 :=
   by
@@ -381,6 +535,12 @@ theorem isUnit_or_eq_zero_of_separable_expand {f : F[X]} (n : ℕ) (hp : 0 < p)
   rwa [hrf, is_unit_C]
 #align polynomial.is_unit_or_eq_zero_of_separable_expand Polynomial.isUnit_or_eq_zero_of_separable_expand
 
+/- warning: polynomial.unique_separable_of_irreducible -> Polynomial.unique_separable_of_irreducible is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (p : Nat) [HF : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) p] {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f) -> (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) p) -> (forall (n₁ : Nat) (g₁ : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))), (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) g₁) -> (Eq.{succ u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (fun (_x : AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) => (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) -> (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) ([anonymous].{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n₁)) g₁) f) -> (forall (n₂ : Nat) (g₂ : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))), (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) g₂) -> (Eq.{succ u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (fun (_x : AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) => (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) -> (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) ([anonymous].{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p n₂)) g₂) f) -> (And (Eq.{1} Nat n₁ n₂) (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) g₁ g₂))))
+but is expected to have type
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (p : Nat) [HF : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (Ring.toAddGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) p] {f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) f) -> (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) p) -> (forall (n₁ : Nat) (g₁ : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))), (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) g₁) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) g₁) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AlgHom.algHomClass.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n₁)) g₁) f) -> (forall (n₂ : Nat) (g₂ : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))), (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) g₂) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) g₂) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (fun (_x : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AlgHom.algHomClass.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p n₂)) g₂) f) -> (And (Eq.{1} Nat n₁ n₂) (Eq.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) g₁ g₂))))
+Case conversion may be inaccurate. Consider using '#align polynomial.unique_separable_of_irreducible Polynomial.unique_separable_of_irreducibleₓ'. -/
 theorem unique_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : 0 < p) (n₁ : ℕ)
     (g₁ : F[X]) (hg₁ : g₁.Separable) (hgf₁ : expand F (p ^ n₁) g₁ = f) (n₂ : ℕ) (g₂ : F[X])
     (hg₂ : g₂.Separable) (hgf₂ : expand F (p ^ n₂) g₂ = f) : n₁ = n₂ ∧ g₁ = g₂ :=
@@ -407,16 +567,28 @@ theorem unique_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : 0
 
 end CharP
 
+/- warning: polynomial.separable_X_pow_sub_C -> Polynomial.separable_X_pow_sub_C is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {n : Nat} (a : F), (Ne.{succ u1} F ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat F (HasLiftT.mk.{1, succ u1} Nat F (CoeTCₓ.coe.{1, succ u1} Nat F (Nat.castCoe.{u1} F (AddMonoidWithOne.toNatCast.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))) n) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Ne.{succ u1} F a (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) Nat (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHPow.{u1, 0} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.X.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) n) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) a)))
+but is expected to have type
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {n : Nat} (a : F), (Ne.{succ u1} F (Nat.cast.{u1} F (Semiring.toNatCast.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) n) (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (CommMonoidWithZero.toZero.{u1} F (CommGroupWithZero.toCommMonoidWithZero.{u1} F (Semifield.toCommGroupWithZero.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) -> (Ne.{succ u1} F a (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (CommMonoidWithZero.toZero.{u1} F (CommGroupWithZero.toCommMonoidWithZero.{u1} F (Semifield.toCommGroupWithZero.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) -> (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) a) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) Nat (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHPow.{u1, 0} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Polynomial.X.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) n) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) a)))
+Case conversion may be inaccurate. Consider using '#align polynomial.separable_X_pow_sub_C Polynomial.separable_X_pow_sub_Cₓ'. -/
 /-- If `n ≠ 0` in `F`, then ` X ^ n - a` is separable for any `a ≠ 0`. -/
-theorem separable_x_pow_sub_c {n : ℕ} (a : F) (hn : (n : F) ≠ 0) (ha : a ≠ 0) :
+theorem separable_X_pow_sub_C {n : ℕ} (a : F) (hn : (n : F) ≠ 0) (ha : a ≠ 0) :
     Separable (X ^ n - C a) :=
-  separable_x_pow_sub_c_unit (Units.mk0 a ha) (IsUnit.mk0 n hn)
-#align polynomial.separable_X_pow_sub_C Polynomial.separable_x_pow_sub_c
-
+  separable_X_pow_sub_C_unit (Units.mk0 a ha) (IsUnit.mk0 n hn)
+#align polynomial.separable_X_pow_sub_C Polynomial.separable_X_pow_sub_C
+
+/- warning: polynomial.X_pow_sub_one_separable_iff -> Polynomial.X_pow_sub_one_separable_iff is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {n : Nat}, Iff (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) Nat (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHPow.{u1, 0} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.X.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) n) (OfNat.ofNat.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 1 (OfNat.mk.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) 1 (One.one.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.hasOne.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))) (Ne.{succ u1} F ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat F (HasLiftT.mk.{1, succ u1} Nat F (CoeTCₓ.coe.{1, succ u1} Nat F (Nat.castCoe.{u1} F (AddMonoidWithOne.toNatCast.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))) n) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))))))))
+but is expected to have type
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {n : Nat}, Iff (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) Nat (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHPow.{u1, 0} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) Nat (Monoid.Pow.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Polynomial.X.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) n) (OfNat.ofNat.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.one.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Ne.{succ u1} F (Nat.cast.{u1} F (Semiring.toNatCast.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) n) (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (CommMonoidWithZero.toZero.{u1} F (CommGroupWithZero.toCommMonoidWithZero.{u1} F (Semifield.toCommGroupWithZero.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.X_pow_sub_one_separable_iff Polynomial.X_pow_sub_one_separable_iffₓ'. -/
 -- this can possibly be strengthened to making `separable_X_pow_sub_C_unit` a
 -- bi-implication, but it is nontrivial!
 /-- In a field `F`, `X ^ n - 1` is separable iff `↑n ≠ 0`. -/
-theorem x_pow_sub_one_separable_iff {n : ℕ} : (X ^ n - 1 : F[X]).Separable ↔ (n : F) ≠ 0 :=
+theorem X_pow_sub_one_separable_iff {n : ℕ} : (X ^ n - 1 : F[X]).Separable ↔ (n : F) ≠ 0 :=
   by
   refine' ⟨_, fun h => separable_X_pow_sub_C_unit 1 (IsUnit.mk0 (↑n) h)⟩
   rw [separable_def', derivative_sub, derivative_X_pow, derivative_one, sub_zero]
@@ -424,10 +596,11 @@ theorem x_pow_sub_one_separable_iff {n : ℕ} : (X ^ n - 1 : F[X]).Separable ↔
   rintro (h : IsCoprime _ _) hn'
   rw [hn', C_0, MulZeroClass.zero_mul, isCoprime_zero_right] at h
   exact not_is_unit_X_pow_sub_one F n h
-#align polynomial.X_pow_sub_one_separable_iff Polynomial.x_pow_sub_one_separable_iff
+#align polynomial.X_pow_sub_one_separable_iff Polynomial.X_pow_sub_one_separable_iff
 
 section Splits
 
+#print Polynomial.card_rootSet_eq_natDegree /-
 theorem card_rootSet_eq_natDegree [Algebra F K] {p : F[X]} (hsep : p.Separable)
     (hsplit : Splits (algebraMap F K) p) : Fintype.card (p.rootSet K) = p.natDegree :=
   by
@@ -435,10 +608,17 @@ theorem card_rootSet_eq_natDegree [Algebra F K] {p : F[X]} (hsep : p.Separable)
   rw [Multiset.toFinset_card_of_nodup, ← nat_degree_eq_card_roots hsplit]
   exact nodup_roots hsep.map
 #align polynomial.card_root_set_eq_nat_degree Polynomial.card_rootSet_eq_natDegree
+-/
 
 variable {i : F →+* K}
 
-theorem eq_x_sub_c_of_separable_of_root_eq {x : F} {h : F[X]} (h_sep : h.Separable)
+/- warning: polynomial.eq_X_sub_C_of_separable_of_root_eq -> Polynomial.eq_X_sub_C_of_separable_of_root_eq is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {K : Type.{u2}} [_inst_2 : Field.{u2} K] {i : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : F} {h : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) h) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) x h) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Polynomial.Splits.{u1, u2} F K (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)) _inst_2 i h) -> (forall (y : K), (Membership.Mem.{u2, u2} K (Multiset.{u2} K) (Multiset.hasMem.{u2} K) y (Polynomial.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Polynomial.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) i h))) -> (Eq.{succ u2} K y (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) i x))) -> (Eq.{succ u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) h (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHMul.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.mul'.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.leadingCoeff.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) h)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (fun (_x : RingHom.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) => F -> (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) (RingHom.hasCoeToFun.{u1, u1} F (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))) (Polynomial.C.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) x))))
+but is expected to have type
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {K : Type.{u2}} [_inst_2 : Field.{u2} K] {i : RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))} {x : F} {h : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))}, (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) h) -> (Eq.{succ u1} F (Polynomial.eval.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) x h) (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (CommMonoidWithZero.toZero.{u1} F (CommGroupWithZero.toCommMonoidWithZero.{u1} F (Semifield.toCommGroupWithZero.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) -> (Polynomial.Splits.{u1, u2} F K (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)) _inst_2 i h) -> (forall (y : K), (Membership.mem.{u2, u2} K (Multiset.{u2} K) (Multiset.instMembershipMultiset.{u2} K) y (Polynomial.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Polynomial.map.{u1, u2} F K (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))) i h))) -> (Eq.{succ u2} K y (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))))) i x))) -> (Eq.{succ u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) h (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) h)) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) h)) (Polynomial.mul'.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) h)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) x) (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (instHSub.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.sub.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.X.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (RingHom.instRingHomClassRingHom.{u1, u1} F (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.C.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) x))))
+Case conversion may be inaccurate. Consider using '#align polynomial.eq_X_sub_C_of_separable_of_root_eq Polynomial.eq_X_sub_C_of_separable_of_root_eqₓ'. -/
+theorem eq_X_sub_C_of_separable_of_root_eq {x : F} {h : F[X]} (h_sep : h.Separable)
     (h_root : h.eval x = 0) (h_splits : Splits i h) (h_roots : ∀ y ∈ (h.map i).roots, y = i x) :
     h = C (leadingCoeff h) * (X - C x) :=
   by
@@ -456,8 +636,14 @@ theorem eq_x_sub_c_of_separable_of_root_eq {x : F} {h : F[X]} (h_sep : h.Separab
       exact RingHom.map_zero i
     · exact h_roots
   · exact nodup_roots (separable.map h_sep)
-#align polynomial.eq_X_sub_C_of_separable_of_root_eq Polynomial.eq_x_sub_c_of_separable_of_root_eq
-
+#align polynomial.eq_X_sub_C_of_separable_of_root_eq Polynomial.eq_X_sub_C_of_separable_of_root_eq
+
+/- warning: polynomial.exists_finset_of_splits -> Polynomial.exists_finset_of_splits is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {K : Type.{u2}} [_inst_2 : Field.{u2} K] (i : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) f) -> (Polynomial.Splits.{u1, u2} F K (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)) _inst_2 i f) -> (Exists.{succ u2} (Finset.{u2} K) (fun (s : Finset.{u2} K) => Eq.{succ u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) i f) (HMul.hMul.{u2, u2, u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (instHMul.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.mul'.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (fun (_x : RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) => K -> (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (Polynomial.C.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) i (Polynomial.leadingCoeff.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) f))) (Finset.prod.{u2, u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) K (CommRing.toCommMonoid.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.commRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)))) s (fun (a : K) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (instHSub.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.sub.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.X.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (fun (_x : RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) => K -> (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (Polynomial.C.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) a))))))
+but is expected to have type
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] {K : Type.{u2}} [_inst_2 : Field.{u2} K] (i : RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) {f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))}, (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) f) -> (Polynomial.Splits.{u1, u2} F K (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)) _inst_2 i f) -> (Exists.{succ u2} (Finset.{u2} K) (fun (s : Finset.{u2} K) => Eq.{succ u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Polynomial.map.{u1, u2} F K (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _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 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f))) (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f))) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f))) (Polynomial.mul'.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2))))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2))))))))) (Polynomial.C.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (DivisionSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Semifield.toDivisionSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f)) _inst_2)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u1} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} F (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))))) i (Polynomial.leadingCoeff.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) f))) (Finset.prod.{u2, u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) K (CommRing.toCommMonoid.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Polynomial.commRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)))) s (fun (a : K) => HSub.hSub.{u2, u2, u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) a) (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (instHSub.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Polynomial.sub.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.X.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} K (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} K (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))) K (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} K (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))) K (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} K (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))))) K (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u2, u2} K (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))))))) (Polynomial.C.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) a))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.exists_finset_of_splits Polynomial.exists_finset_of_splitsₓ'. -/
 theorem exists_finset_of_splits (i : F →+* K) {f : F[X]} (sep : Separable f) (sp : Splits i f) :
     ∃ s : Finset K, f.map i = C (i f.leadingCoeff) * s.Prod fun a : K => X - C a :=
   by
@@ -472,6 +658,12 @@ theorem exists_finset_of_splits (i : F →+* K) {f : F[X]} (sep : Separable f) (
 
 end Splits
 
+/- warning: irreducible.separable -> Irreducible.separable is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] [_inst_3 : CharZero.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))] {f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f) -> (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) f)
+but is expected to have type
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] [_inst_3 : CharZero.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (Ring.toAddGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))] {f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))}, (Irreducible.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) f) -> (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) f)
+Case conversion may be inaccurate. Consider using '#align irreducible.separable Irreducible.separableₓ'. -/
 theorem Irreducible.separable [CharZero F] {f : F[X]} (hf : Irreducible f) : f.Separable :=
   by
   rw [separable_iff_derivative_ne_zero hf, Ne, ← degree_eq_bot, degree_derivative_eq]
@@ -494,6 +686,7 @@ section CommRing
 
 variable (F K : Type _) [CommRing F] [Ring K] [Algebra F K]
 
+#print IsSeparable /-
 -- TODO: refactor to allow transcendental extensions?
 -- See: https://en.wikipedia.org/wiki/Separable_extension#Separability_of_transcendental_extensions
 -- Note that right now a Galois extension (class `is_galois`) is defined to be an extension which
@@ -509,19 +702,38 @@ class IsSeparable : Prop where
   is_integral' (x : K) : IsIntegral F x
   separable' (x : K) : (minpoly F x).Separable
 #align is_separable IsSeparable
+-/
 
 variable (F) {K}
 
+/- warning: is_separable.is_integral -> IsSeparable.isIntegral is a dubious translation:
+lean 3 declaration is
+  forall (F : Type.{u1}) {K : Type.{u2}} [_inst_1 : CommRing.{u1} F] [_inst_2 : Ring.{u2} K] [_inst_3 : Algebra.{u1, u2} F K (CommRing.toCommSemiring.{u1} F _inst_1) (Ring.toSemiring.{u2} K _inst_2)] [_inst_4 : IsSeparable.{u1, u2} F K _inst_1 _inst_2 _inst_3] (x : K), IsIntegral.{u1, u2} F K _inst_1 _inst_2 _inst_3 x
+but is expected to have type
+  forall (F : Type.{u2}) {K : Type.{u1}} [_inst_1 : CommRing.{u2} F] [_inst_2 : Ring.{u1} K] [_inst_3 : Algebra.{u2, u1} F K (CommRing.toCommSemiring.{u2} F _inst_1) (Ring.toSemiring.{u1} K _inst_2)] [_inst_4 : IsSeparable.{u2, u1} F K _inst_1 _inst_2 _inst_3] (x : K), IsIntegral.{u2, u1} F K _inst_1 _inst_2 _inst_3 x
+Case conversion may be inaccurate. Consider using '#align is_separable.is_integral IsSeparable.isIntegralₓ'. -/
 theorem IsSeparable.isIntegral [IsSeparable F K] : ∀ x : K, IsIntegral F x :=
   IsSeparable.is_integral'
 #align is_separable.is_integral IsSeparable.isIntegral
 
+/- warning: is_separable.separable -> IsSeparable.separable is a dubious translation:
+lean 3 declaration is
+  forall (F : Type.{u1}) {K : Type.{u2}} [_inst_1 : CommRing.{u1} F] [_inst_2 : Ring.{u2} K] [_inst_3 : Algebra.{u1, u2} F K (CommRing.toCommSemiring.{u1} F _inst_1) (Ring.toSemiring.{u2} K _inst_2)] [_inst_4 : IsSeparable.{u1, u2} F K _inst_1 _inst_2 _inst_3] (x : K), Polynomial.Separable.{u1} F (CommRing.toCommSemiring.{u1} F _inst_1) (minpoly.{u1, u2} F K _inst_1 _inst_2 _inst_3 x)
+but is expected to have type
+  forall (F : Type.{u2}) {K : Type.{u1}} [_inst_1 : CommRing.{u2} F] [_inst_2 : Ring.{u1} K] [_inst_3 : Algebra.{u2, u1} F K (CommRing.toCommSemiring.{u2} F _inst_1) (Ring.toSemiring.{u1} K _inst_2)] [_inst_4 : IsSeparable.{u2, u1} F K _inst_1 _inst_2 _inst_3] (x : K), Polynomial.Separable.{u2} F (CommRing.toCommSemiring.{u2} F _inst_1) (minpoly.{u2, u1} F K _inst_1 _inst_2 _inst_3 x)
+Case conversion may be inaccurate. Consider using '#align is_separable.separable IsSeparable.separableₓ'. -/
 theorem IsSeparable.separable [IsSeparable F K] : ∀ x : K, (minpoly F x).Separable :=
   IsSeparable.separable'
 #align is_separable.separable IsSeparable.separable
 
 variable {F K}
 
+/- warning: is_separable_iff -> isSeparable_iff is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} {K : Type.{u2}} [_inst_1 : CommRing.{u1} F] [_inst_2 : Ring.{u2} K] [_inst_3 : Algebra.{u1, u2} F K (CommRing.toCommSemiring.{u1} F _inst_1) (Ring.toSemiring.{u2} K _inst_2)], Iff (IsSeparable.{u1, u2} F K _inst_1 _inst_2 _inst_3) (forall (x : K), And (IsIntegral.{u1, u2} F K _inst_1 _inst_2 _inst_3 x) (Polynomial.Separable.{u1} F (CommRing.toCommSemiring.{u1} F _inst_1) (minpoly.{u1, u2} F K _inst_1 _inst_2 _inst_3 x)))
+but is expected to have type
+  forall {F : Type.{u2}} {K : Type.{u1}} [_inst_1 : CommRing.{u2} F] [_inst_2 : Ring.{u1} K] [_inst_3 : Algebra.{u2, u1} F K (CommRing.toCommSemiring.{u2} F _inst_1) (Ring.toSemiring.{u1} K _inst_2)], Iff (IsSeparable.{u2, u1} F K _inst_1 _inst_2 _inst_3) (forall (x : K), And (IsIntegral.{u2, u1} F K _inst_1 _inst_2 _inst_3 x) (Polynomial.Separable.{u2} F (CommRing.toCommSemiring.{u2} F _inst_1) (minpoly.{u2, u1} F K _inst_1 _inst_2 _inst_3 x)))
+Case conversion may be inaccurate. Consider using '#align is_separable_iff isSeparable_iffₓ'. -/
 theorem isSeparable_iff : IsSeparable F K ↔ ∀ x : K, IsIntegral F x ∧ (minpoly F x).Separable :=
   ⟨fun h x => ⟨@IsSeparable.isIntegral F _ _ _ h x, @IsSeparable.separable F _ _ _ h x⟩, fun h =>
     ⟨fun x => (h x).1, fun x => (h x).2⟩⟩
@@ -529,13 +741,21 @@ theorem isSeparable_iff : IsSeparable F K ↔ ∀ x : K, IsIntegral F x ∧ (min
 
 end CommRing
 
+#print isSeparable_self /-
 instance isSeparable_self (F : Type _) [Field F] : IsSeparable F F :=
   ⟨fun x => isIntegral_algebraMap, fun x =>
     by
     rw [minpoly.eq_X_sub_C']
     exact separable_X_sub_C⟩
 #align is_separable_self isSeparable_self
+-/
 
+/- warning: is_separable.of_finite -> IsSeparable.of_finite is a dubious translation:
+lean 3 declaration is
+  forall (F : Type.{u1}) (K : Type.{u2}) [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] [_inst_3 : Algebra.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))] [_inst_4 : FiniteDimensional.{u1, u2} F K (Field.toDivisionRing.{u1} F _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (Algebra.toModule.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) _inst_3)] [_inst_5 : CharZero.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))))], IsSeparable.{u1, u2} F K (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)) (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)) _inst_3
+but is expected to have type
+  forall (F : Type.{u1}) (K : Type.{u2}) [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] [_inst_3 : Algebra.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))] [_inst_4 : FiniteDimensional.{u1, u2} F K (Field.toDivisionRing.{u1} F _inst_1) (Ring.toAddCommGroup.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) (Algebra.toModule.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))) _inst_3)] [_inst_5 : CharZero.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (Ring.toAddGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))], IsSeparable.{u1, u2} F K (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)) (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)) _inst_3
+Case conversion may be inaccurate. Consider using '#align is_separable.of_finite IsSeparable.of_finiteₓ'. -/
 -- See note [lower instance priority]
 /-- A finite field extension in characteristic 0 is separable. -/
 instance (priority := 100) IsSeparable.of_finite (F K : Type _) [Field F] [Field K] [Algebra F K]
@@ -549,11 +769,23 @@ section IsSeparableTower
 variable (F K E : Type _) [Field F] [Field K] [Field E] [Algebra F K] [Algebra F E] [Algebra K E]
   [IsScalarTower F K E]
 
+/- warning: is_separable_tower_top_of_is_separable -> isSeparable_tower_top_of_isSeparable is a dubious translation:
+lean 3 declaration is
+  forall (F : Type.{u1}) (K : Type.{u2}) (E : Type.{u3}) [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] [_inst_3 : Field.{u3} E] [_inst_4 : Algebra.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))] [_inst_5 : Algebra.{u1, u3} F E (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3)))] [_inst_6 : Algebra.{u2, u3} K E (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)) (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3)))] [_inst_7 : IsScalarTower.{u1, u2, u3} F K E (SMulZeroClass.toHasSmul.{u1, u2} F K (AddZeroClass.toHasZero.{u2} K (AddMonoid.toAddZeroClass.{u2} K (AddCommMonoid.toAddMonoid.{u2} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} F K (MulZeroClass.toHasZero.{u1} F (MulZeroOneClass.toMulZeroClass.{u1} F (MonoidWithZero.toMulZeroOneClass.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (AddZeroClass.toHasZero.{u2} K (AddMonoid.toAddZeroClass.{u2} K (AddCommMonoid.toAddMonoid.{u2} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} F K (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddZeroClass.toHasZero.{u2} K (AddMonoid.toAddZeroClass.{u2} K (AddCommMonoid.toAddMonoid.{u2} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))))) (Module.toMulActionWithZero.{u1, u2} F K (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (Algebra.toModule.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} K E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))))))))) (SMulWithZero.toSmulZeroClass.{u2, u3} K E (MulZeroClass.toHasZero.{u2} K (MulZeroOneClass.toMulZeroClass.{u2} K (MonoidWithZero.toMulZeroOneClass.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))))))))) (MulActionWithZero.toSMulWithZero.{u2, u3} K E (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))))))))) (Module.toMulActionWithZero.{u2, u3} K E (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3)))))) (Algebra.toModule.{u2, u3} K E (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)) (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} F E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} F E (MulZeroClass.toHasZero.{u1} F (MulZeroOneClass.toMulZeroClass.{u1} F (MonoidWithZero.toMulZeroOneClass.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} F E (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))))))))) (Module.toMulActionWithZero.{u1, u3} F E (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3)))))) (Algebra.toModule.{u1, u3} F E (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))) _inst_5)))))] [_inst_8 : IsSeparable.{u1, u3} F E (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)) (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3)) _inst_5], IsSeparable.{u2, u3} K E (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3)) _inst_6
+but is expected to have type
+  forall (F : Type.{u3}) (K : Type.{u1}) (E : Type.{u2}) [_inst_1 : Field.{u3} F] [_inst_2 : Field.{u1} K] [_inst_3 : Field.{u2} E] [_inst_4 : Algebra.{u3, u1} F K (Semifield.toCommSemiring.{u3} F (Field.toSemifield.{u3} F _inst_1)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))] [_inst_5 : Algebra.{u3, u2} F E (Semifield.toCommSemiring.{u3} F (Field.toSemifield.{u3} F _inst_1)) (DivisionSemiring.toSemiring.{u2} E (Semifield.toDivisionSemiring.{u2} E (Field.toSemifield.{u2} E _inst_3)))] [_inst_6 : Algebra.{u1, u2} K E (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)) (DivisionSemiring.toSemiring.{u2} E (Semifield.toDivisionSemiring.{u2} E (Field.toSemifield.{u2} E _inst_3)))] [_inst_7 : IsScalarTower.{u3, u1, u2} F K E (Algebra.toSMul.{u3, u1} F K (Semifield.toCommSemiring.{u3} F (Field.toSemifield.{u3} F _inst_1)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) _inst_4) (Algebra.toSMul.{u1, u2} K E (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)) (DivisionSemiring.toSemiring.{u2} E (Semifield.toDivisionSemiring.{u2} E (Field.toSemifield.{u2} E _inst_3))) _inst_6) (Algebra.toSMul.{u3, u2} F E (Semifield.toCommSemiring.{u3} F (Field.toSemifield.{u3} F _inst_1)) (DivisionSemiring.toSemiring.{u2} E (Semifield.toDivisionSemiring.{u2} E (Field.toSemifield.{u2} E _inst_3))) _inst_5)] [_inst_8 : IsSeparable.{u3, u2} F E (EuclideanDomain.toCommRing.{u3} F (Field.toEuclideanDomain.{u3} F _inst_1)) (DivisionRing.toRing.{u2} E (Field.toDivisionRing.{u2} E _inst_3)) _inst_5], IsSeparable.{u1, u2} K E (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (DivisionRing.toRing.{u2} E (Field.toDivisionRing.{u2} E _inst_3)) _inst_6
+Case conversion may be inaccurate. Consider using '#align is_separable_tower_top_of_is_separable isSeparable_tower_top_of_isSeparableₓ'. -/
 theorem isSeparable_tower_top_of_isSeparable [IsSeparable F E] : IsSeparable K E :=
   ⟨fun x => isIntegral_of_isScalarTower (IsSeparable.isIntegral F x), fun x =>
     (IsSeparable.separable F x).map.of_dvd (minpoly.dvd_map_of_isScalarTower _ _ _)⟩
 #align is_separable_tower_top_of_is_separable isSeparable_tower_top_of_isSeparable
 
+/- warning: is_separable_tower_bot_of_is_separable -> isSeparable_tower_bot_of_isSeparable is a dubious translation:
+lean 3 declaration is
+  forall (F : Type.{u1}) (K : Type.{u2}) (E : Type.{u3}) [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] [_inst_3 : Field.{u3} E] [_inst_4 : Algebra.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))] [_inst_5 : Algebra.{u1, u3} F E (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3)))] [_inst_6 : Algebra.{u2, u3} K E (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)) (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3)))] [_inst_7 : IsScalarTower.{u1, u2, u3} F K E (SMulZeroClass.toHasSmul.{u1, u2} F K (AddZeroClass.toHasZero.{u2} K (AddMonoid.toAddZeroClass.{u2} K (AddCommMonoid.toAddMonoid.{u2} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} F K (MulZeroClass.toHasZero.{u1} F (MulZeroOneClass.toMulZeroClass.{u1} F (MonoidWithZero.toMulZeroOneClass.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (AddZeroClass.toHasZero.{u2} K (AddMonoid.toAddZeroClass.{u2} K (AddCommMonoid.toAddMonoid.{u2} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} F K (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddZeroClass.toHasZero.{u2} K (AddMonoid.toAddZeroClass.{u2} K (AddCommMonoid.toAddMonoid.{u2} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))))) (Module.toMulActionWithZero.{u1, u2} F K (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (Algebra.toModule.{u1, u2} F K (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} K E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))))))))) (SMulWithZero.toSmulZeroClass.{u2, u3} K E (MulZeroClass.toHasZero.{u2} K (MulZeroOneClass.toMulZeroClass.{u2} K (MonoidWithZero.toMulZeroOneClass.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))))))))) (MulActionWithZero.toSMulWithZero.{u2, u3} K E (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))))))))) (Module.toMulActionWithZero.{u2, u3} K E (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3)))))) (Algebra.toModule.{u2, u3} K E (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)) (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} F E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} F E (MulZeroClass.toHasZero.{u1} F (MulZeroOneClass.toMulZeroClass.{u1} F (MonoidWithZero.toMulZeroOneClass.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} F E (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))))))))) (Module.toMulActionWithZero.{u1, u3} F E (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} E (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} E (Semiring.toNonAssocSemiring.{u3} E (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3)))))) (Algebra.toModule.{u1, u3} F E (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Ring.toSemiring.{u3} E (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3))) _inst_5)))))] [h : IsSeparable.{u1, u3} F E (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)) (DivisionRing.toRing.{u3} E (Field.toDivisionRing.{u3} E _inst_3)) _inst_5], IsSeparable.{u1, u2} F K (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)) (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)) _inst_4
+but is expected to have type
+  forall (F : Type.{u3}) (K : Type.{u1}) (E : Type.{u2}) [_inst_1 : Field.{u3} F] [_inst_2 : Field.{u1} K] [_inst_3 : Field.{u2} E] [_inst_4 : Algebra.{u3, u1} F K (Semifield.toCommSemiring.{u3} F (Field.toSemifield.{u3} F _inst_1)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))] [_inst_5 : Algebra.{u3, u2} F E (Semifield.toCommSemiring.{u3} F (Field.toSemifield.{u3} F _inst_1)) (DivisionSemiring.toSemiring.{u2} E (Semifield.toDivisionSemiring.{u2} E (Field.toSemifield.{u2} E _inst_3)))] [_inst_6 : Algebra.{u1, u2} K E (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)) (DivisionSemiring.toSemiring.{u2} E (Semifield.toDivisionSemiring.{u2} E (Field.toSemifield.{u2} E _inst_3)))] [_inst_7 : IsScalarTower.{u3, u1, u2} F K E (Algebra.toSMul.{u3, u1} F K (Semifield.toCommSemiring.{u3} F (Field.toSemifield.{u3} F _inst_1)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) _inst_4) (Algebra.toSMul.{u1, u2} K E (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)) (DivisionSemiring.toSemiring.{u2} E (Semifield.toDivisionSemiring.{u2} E (Field.toSemifield.{u2} E _inst_3))) _inst_6) (Algebra.toSMul.{u3, u2} F E (Semifield.toCommSemiring.{u3} F (Field.toSemifield.{u3} F _inst_1)) (DivisionSemiring.toSemiring.{u2} E (Semifield.toDivisionSemiring.{u2} E (Field.toSemifield.{u2} E _inst_3))) _inst_5)] [h : IsSeparable.{u3, u2} F E (EuclideanDomain.toCommRing.{u3} F (Field.toEuclideanDomain.{u3} F _inst_1)) (DivisionRing.toRing.{u2} E (Field.toDivisionRing.{u2} E _inst_3)) _inst_5], IsSeparable.{u3, u1} F K (EuclideanDomain.toCommRing.{u3} F (Field.toEuclideanDomain.{u3} F _inst_1)) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)) _inst_4
+Case conversion may be inaccurate. Consider using '#align is_separable_tower_bot_of_is_separable isSeparable_tower_bot_of_isSeparableₓ'. -/
 theorem isSeparable_tower_bot_of_isSeparable [h : IsSeparable F E] : IsSeparable F K :=
   isSeparable_iff.2 fun x =>
     by
@@ -569,6 +801,12 @@ theorem isSeparable_tower_bot_of_isSeparable [h : IsSeparable F E] : IsSeparable
 
 variable {E}
 
+/- warning: is_separable.of_alg_hom -> IsSeparable.of_algHom is a dubious translation:
+lean 3 declaration is
+  forall (F : Type.{u1}) {E : Type.{u2}} [_inst_1 : Field.{u1} F] [_inst_3 : Field.{u2} E] [_inst_5 : Algebra.{u1, u2} F E (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Ring.toSemiring.{u2} E (DivisionRing.toRing.{u2} E (Field.toDivisionRing.{u2} E _inst_3)))] (E' : Type.{u3}) [_inst_8 : Field.{u3} E'] [_inst_9 : Algebra.{u1, u3} F E' (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Ring.toSemiring.{u3} E' (DivisionRing.toRing.{u3} E' (Field.toDivisionRing.{u3} E' _inst_8)))], (AlgHom.{u1, u2, u3} F E E' (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Ring.toSemiring.{u2} E (DivisionRing.toRing.{u2} E (Field.toDivisionRing.{u2} E _inst_3))) (Ring.toSemiring.{u3} E' (DivisionRing.toRing.{u3} E' (Field.toDivisionRing.{u3} E' _inst_8))) _inst_5 _inst_9) -> (forall [_inst_10 : IsSeparable.{u1, u3} F E' (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)) (DivisionRing.toRing.{u3} E' (Field.toDivisionRing.{u3} E' _inst_8)) _inst_9], IsSeparable.{u1, u2} F E (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)) (DivisionRing.toRing.{u2} E (Field.toDivisionRing.{u2} E _inst_3)) _inst_5)
+but is expected to have type
+  forall (F : Type.{u2}) {E : Type.{u1}} [_inst_1 : Field.{u2} F] [_inst_3 : Field.{u1} E] [_inst_5 : Algebra.{u2, u1} F E (Semifield.toCommSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)) (DivisionSemiring.toSemiring.{u1} E (Semifield.toDivisionSemiring.{u1} E (Field.toSemifield.{u1} E _inst_3)))] (E' : Type.{u3}) [_inst_8 : Field.{u3} E'] [_inst_9 : Algebra.{u2, u3} F E' (Semifield.toCommSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)) (DivisionSemiring.toSemiring.{u3} E' (Semifield.toDivisionSemiring.{u3} E' (Field.toSemifield.{u3} E' _inst_8)))], (AlgHom.{u2, u1, u3} F E E' (Semifield.toCommSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)) (DivisionSemiring.toSemiring.{u1} E (Semifield.toDivisionSemiring.{u1} E (Field.toSemifield.{u1} E _inst_3))) (DivisionSemiring.toSemiring.{u3} E' (Semifield.toDivisionSemiring.{u3} E' (Field.toSemifield.{u3} E' _inst_8))) _inst_5 _inst_9) -> (forall [_inst_10 : IsSeparable.{u2, u3} F E' (EuclideanDomain.toCommRing.{u2} F (Field.toEuclideanDomain.{u2} F _inst_1)) (DivisionRing.toRing.{u3} E' (Field.toDivisionRing.{u3} E' _inst_8)) _inst_9], IsSeparable.{u2, u1} F E (EuclideanDomain.toCommRing.{u2} F (Field.toEuclideanDomain.{u2} F _inst_1)) (DivisionRing.toRing.{u1} E (Field.toDivisionRing.{u1} E _inst_3)) _inst_5)
+Case conversion may be inaccurate. Consider using '#align is_separable.of_alg_hom IsSeparable.of_algHomₓ'. -/
 theorem IsSeparable.of_algHom (E' : Type _) [Field E'] [Algebra F E'] (f : E →ₐ[F] E')
     [IsSeparable F E'] : IsSeparable F E :=
   by
@@ -587,6 +825,12 @@ variable {K L F : Type _} [Field K] [Field L] [Field F]
 
 variable [Algebra K S] [Algebra K L]
 
+/- warning: alg_hom.card_of_power_basis -> AlgHom.card_of_powerBasis is a dubious translation:
+lean 3 declaration is
+  forall {S : Type.{u1}} [_inst_1 : CommRing.{u1} S] {K : Type.{u2}} {L : Type.{u3}} [_inst_2 : Field.{u2} K] [_inst_3 : Field.{u3} L] [_inst_5 : Algebra.{u2, u1} K S (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_1))] [_inst_6 : Algebra.{u2, u3} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)) (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_3)))] (pb : PowerBasis.{u2, u1} K S (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (CommRing.toRing.{u1} S _inst_1) _inst_5), (Polynomial.Separable.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)) (minpoly.{u2, u1} K S (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (CommRing.toRing.{u1} S _inst_1) _inst_5 (PowerBasis.gen.{u2, u1} K S (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (CommRing.toRing.{u1} S _inst_1) _inst_5 pb))) -> (Polynomial.Splits.{u2, u3} K L (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) _inst_3 (algebraMap.{u2, u3} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)) (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_3))) _inst_6) (minpoly.{u2, u1} K S (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (CommRing.toRing.{u1} S _inst_1) _inst_5 (PowerBasis.gen.{u2, u1} K S (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (CommRing.toRing.{u1} S _inst_1) _inst_5 pb))) -> (Eq.{1} Nat (Fintype.card.{max u1 u3} (AlgHom.{u2, u1, u3} K S L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_1)) (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_3))) _inst_5 _inst_6) (PowerBasis.AlgHom.fintype.{u1, u2, u3} S (CommRing.toRing.{u1} S _inst_1) K L (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (EuclideanDomain.toCommRing.{u3} L (Field.toEuclideanDomain.{u3} L _inst_3)) (Field.isDomain.{u3} L _inst_3) _inst_6 _inst_5 pb)) (PowerBasis.dim.{u2, u1} K S (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (CommRing.toRing.{u1} S _inst_1) _inst_5 pb))
+but is expected to have type
+  forall {S : Type.{u2}} [_inst_1 : CommRing.{u2} S] {K : Type.{u3}} {L : Type.{u1}} [_inst_2 : Field.{u3} K] [_inst_3 : Field.{u1} L] [_inst_5 : Algebra.{u3, u2} K S (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_2)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_1))] [_inst_6 : Algebra.{u3, u1} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_2)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_3)))] (pb : PowerBasis.{u3, u2} K S (EuclideanDomain.toCommRing.{u3} K (Field.toEuclideanDomain.{u3} K _inst_2)) (CommRing.toRing.{u2} S _inst_1) _inst_5), (Polynomial.Separable.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_2)) (minpoly.{u3, u2} K S (EuclideanDomain.toCommRing.{u3} K (Field.toEuclideanDomain.{u3} K _inst_2)) (CommRing.toRing.{u2} S _inst_1) _inst_5 (PowerBasis.gen.{u3, u2} K S (EuclideanDomain.toCommRing.{u3} K (Field.toEuclideanDomain.{u3} K _inst_2)) (CommRing.toRing.{u2} S _inst_1) _inst_5 pb))) -> (Polynomial.Splits.{u3, u1} K L (EuclideanDomain.toCommRing.{u3} K (Field.toEuclideanDomain.{u3} K _inst_2)) _inst_3 (algebraMap.{u3, u1} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_2)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_3))) _inst_6) (minpoly.{u3, u2} K S (EuclideanDomain.toCommRing.{u3} K (Field.toEuclideanDomain.{u3} K _inst_2)) (CommRing.toRing.{u2} S _inst_1) _inst_5 (PowerBasis.gen.{u3, u2} K S (EuclideanDomain.toCommRing.{u3} K (Field.toEuclideanDomain.{u3} K _inst_2)) (CommRing.toRing.{u2} S _inst_1) _inst_5 pb))) -> (Eq.{1} Nat (Fintype.card.{max u1 u2} (AlgHom.{u3, u2, u1} K S L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_2)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_3))) _inst_5 _inst_6) (PowerBasis.AlgHom.fintype.{u2, u3, u1} S (CommRing.toRing.{u2} S _inst_1) K L (EuclideanDomain.toCommRing.{u3} K (Field.toEuclideanDomain.{u3} K _inst_2)) (EuclideanDomain.toCommRing.{u1} L (Field.toEuclideanDomain.{u1} L _inst_3)) (Field.isDomain.{u1} L _inst_3) _inst_6 _inst_5 pb)) (PowerBasis.dim.{u3, u2} K S (EuclideanDomain.toCommRing.{u3} K (Field.toEuclideanDomain.{u3} K _inst_2)) (CommRing.toRing.{u2} S _inst_1) _inst_5 pb))
+Case conversion may be inaccurate. Consider using '#align alg_hom.card_of_power_basis AlgHom.card_of_powerBasisₓ'. -/
 theorem AlgHom.card_of_powerBasis (pb : PowerBasis K S) (h_sep : (minpoly K pb.gen).Separable)
     (h_splits : (minpoly K pb.gen).Splits (algebraMap K L)) :
     @Fintype.card (S →ₐ[K] L) (PowerBasis.AlgHom.fintype pb) = pb.dim :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

@@ -532,7 +532,7 @@ end CommRing
 instance isSeparable_self (F : Type _) [Field F] : IsSeparable F F :=
   ⟨fun x => isIntegral_algebraMap, fun x =>
     by
-    rw [minpoly.eq_x_sub_C']
+    rw [minpoly.eq_X_sub_C']
     exact separable_X_sub_C⟩
 #align is_separable_self isSeparable_self
 

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

@@ -445,7 +445,7 @@ theorem eq_x_sub_c_of_separable_of_root_eq {x : F} {h : F[X]} (h_sep : h.Separab
   have h_ne_zero : h ≠ 0 := by
     rintro rfl
     exact not_separable_zero h_sep
-  apply Polynomial.eq_x_sub_c_of_splits_of_single_root i h_splits
+  apply Polynomial.eq_X_sub_C_of_splits_of_single_root i h_splits
   apply Finset.mk.inj
   · change _ = {i x}
     rw [Finset.eq_singleton_iff_unique_mem]

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

@@ -56,7 +56,7 @@ theorem separable_def' (f : R[X]) : f.Separable ↔ ∃ a b : R[X], a * f + b *
 theorem not_separable_zero [Nontrivial R] : ¬Separable (0 : R[X]) :=
   by
   rintro ⟨x, y, h⟩
-  simpa only [derivative_zero, mul_zero, add_zero, zero_ne_one] using h
+  simpa only [derivative_zero, MulZeroClass.mul_zero, add_zero, zero_ne_one] using h
 #align polynomial.not_separable_zero Polynomial.not_separable_zero
 
 theorem separable_one : (1 : R[X]).Separable :=
@@ -356,7 +356,7 @@ theorem exists_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : p
     have hg1 : g.nat_degree * p = N.succ := by rwa [← nat_degree_expand, hgf]
     have hg2 : g.nat_degree ≠ 0 := by
       intro this
-      rw [this, zero_mul] at hg1
+      rw [this, MulZeroClass.zero_mul] at hg1
       cases hg1
     have hg3 : g.nat_degree < N.succ :=
       by
@@ -373,7 +373,8 @@ theorem isUnit_or_eq_zero_of_separable_expand {f : F[X]} (n : ℕ) (hp : 0 < p)
   rw [or_iff_not_imp_right]
   rintro hn : n ≠ 0
   have hf2 : (expand F (p ^ n) f).derivative = 0 := by
-    rw [derivative_expand, Nat.cast_pow, CharP.cast_eq_zero, zero_pow hn.bot_lt, zero_mul, mul_zero]
+    rw [derivative_expand, Nat.cast_pow, CharP.cast_eq_zero, zero_pow hn.bot_lt,
+      MulZeroClass.zero_mul, MulZeroClass.mul_zero]
   rw [separable_def, hf2, isCoprime_zero_right, is_unit_iff] at hf
   rcases hf with ⟨r, hr, hrf⟩
   rw [eq_comm, expand_eq_C (pow_pos hp _)] at hrf
@@ -421,7 +422,7 @@ theorem x_pow_sub_one_separable_iff {n : ℕ} : (X ^ n - 1 : F[X]).Separable ↔
   rw [separable_def', derivative_sub, derivative_X_pow, derivative_one, sub_zero]
   -- Suppose `(n : F) = 0`, then the derivative is `0`, so `X ^ n - 1` is a unit, contradiction.
   rintro (h : IsCoprime _ _) hn'
-  rw [hn', C_0, zero_mul, isCoprime_zero_right] at h
+  rw [hn', C_0, MulZeroClass.zero_mul, isCoprime_zero_right] at h
   exact not_is_unit_X_pow_sub_one F n h
 #align polynomial.X_pow_sub_one_separable_iff Polynomial.x_pow_sub_one_separable_iff
 

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

@@ -67,19 +67,19 @@ theorem separable_one : (1 : R[X]).Separable :=
 theorem separable_of_subsingleton [Subsingleton R] (f : R[X]) : f.Separable := by simp [separable]
 #align polynomial.separable_of_subsingleton Polynomial.separable_of_subsingleton
 
-theorem separable_x_add_c (a : R) : (x + c a).Separable :=
+theorem separable_x_add_c (a : R) : (X + C a).Separable :=
   by
   rw [separable_def, derivative_add, derivative_X, derivative_C, add_zero]
   exact isCoprime_one_right
 #align polynomial.separable_X_add_C Polynomial.separable_x_add_c
 
-theorem separable_x : (x : R[X]).Separable :=
+theorem separable_x : (X : R[X]).Separable :=
   by
   rw [separable_def, derivative_X]
   exact isCoprime_one_right
 #align polynomial.separable_X Polynomial.separable_x
 
-theorem separable_c (r : R) : (c r).Separable ↔ IsUnit r := by
+theorem separable_c (r : R) : (C r).Separable ↔ IsUnit r := by
   rw [separable_def, derivative_C, isCoprime_zero_right, is_unit_C]
 #align polynomial.separable_C Polynomial.separable_c
 
@@ -177,7 +177,7 @@ section CommRing
 
 variable {R : Type u} [CommRing R]
 
-theorem separable_x_sub_c {x : R} : Separable (x - c x) := by
+theorem separable_x_sub_c {x : R} : Separable (X - C x) := by
   simpa only [sub_eq_add_neg, C_neg] using separable_X_add_C (-x)
 #align polynomial.separable_X_sub_C Polynomial.separable_x_sub_c
 
@@ -205,7 +205,7 @@ theorem separable_prod {ι : Sort _} [Fintype ι] {f : ι → R[X]} (h1 : Pairwi
 #align polynomial.separable_prod Polynomial.separable_prod
 
 theorem Separable.inj_of_prod_x_sub_c [Nontrivial R] {ι : Sort _} {f : ι → R} {s : Finset ι}
-    (hfs : (∏ i in s, x - c (f i)).Separable) {x y : ι} (hx : x ∈ s) (hy : y ∈ s)
+    (hfs : (∏ i in s, X - C (f i)).Separable) {x y : ι} (hx : x ∈ s) (hy : y ∈ s)
     (hfxy : f x = f y) : x = y := by
   by_contra hxy
   rw [← insert_erase hx, prod_insert (not_mem_erase _ _), ←
@@ -215,12 +215,12 @@ theorem Separable.inj_of_prod_x_sub_c [Nontrivial R] {ι : Sort _} {f : ι → R
 #align polynomial.separable.inj_of_prod_X_sub_C Polynomial.Separable.inj_of_prod_x_sub_c
 
 theorem Separable.injective_of_prod_x_sub_c [Nontrivial R] {ι : Sort _} [Fintype ι] {f : ι → R}
-    (hfs : (∏ i, x - c (f i)).Separable) : Function.Injective f := fun x y hfxy =>
+    (hfs : (∏ i, X - C (f i)).Separable) : Function.Injective f := fun x y hfxy =>
   hfs.inj_of_prod_x_sub_c (mem_univ _) (mem_univ _) hfxy
 #align polynomial.separable.injective_of_prod_X_sub_C Polynomial.Separable.injective_of_prod_x_sub_c
 
 theorem nodup_of_separable_prod [Nontrivial R] {s : Multiset R}
-    (hs : Separable (Multiset.map (fun a => x - c a) s).Prod) : s.Nodup :=
+    (hs : Separable (Multiset.map (fun a => X - C a) s).Prod) : s.Nodup :=
   by
   rw [Multiset.nodup_iff_ne_cons_cons]
   rintro a t rfl
@@ -230,7 +230,7 @@ theorem nodup_of_separable_prod [Nontrivial R] {s : Multiset R}
 
 /-- If `is_unit n` in a `comm_ring R`, then `X ^ n - u` is separable for any unit `u`. -/
 theorem separable_x_pow_sub_c_unit {n : ℕ} (u : Rˣ) (hn : IsUnit (n : R)) :
-    Separable (x ^ n - c (u : R)) := by
+    Separable (X ^ n - C (u : R)) := by
   nontriviality R
   rcases n.eq_zero_or_pos with (rfl | hpos)
   · simpa using hn
@@ -299,7 +299,7 @@ theorem separable_map (f : F →+* K) {p : F[X]} : (p.map f).Separable ↔ p.Sep
 #align polynomial.separable_map Polynomial.separable_map
 
 theorem separable_prod_x_sub_c_iff' {ι : Sort _} {f : ι → F} {s : Finset ι} :
-    (∏ i in s, x - c (f i)).Separable ↔ ∀ x ∈ s, ∀ y ∈ s, f x = f y → x = y :=
+    (∏ i in s, X - C (f i)).Separable ↔ ∀ x ∈ s, ∀ y ∈ s, f x = f y → x = y :=
   ⟨fun hfs x hx y hy hfxy => hfs.inj_of_prod_x_sub_c hx hy hfxy, fun H =>
     by
     rw [← prod_attach]
@@ -312,7 +312,7 @@ theorem separable_prod_x_sub_c_iff' {ι : Sort _} {f : ι → F} {s : Finset ι}
 #align polynomial.separable_prod_X_sub_C_iff' Polynomial.separable_prod_x_sub_c_iff'
 
 theorem separable_prod_x_sub_c_iff {ι : Sort _} [Fintype ι] {f : ι → F} :
-    (∏ i, x - c (f i)).Separable ↔ Function.Injective f :=
+    (∏ i, X - C (f i)).Separable ↔ Function.Injective f :=
   separable_prod_x_sub_c_iff'.trans <| by simp_rw [mem_univ, true_imp_iff, Function.Injective]
 #align polynomial.separable_prod_X_sub_C_iff Polynomial.separable_prod_x_sub_c_iff
 
@@ -408,14 +408,14 @@ end CharP
 
 /-- If `n ≠ 0` in `F`, then ` X ^ n - a` is separable for any `a ≠ 0`. -/
 theorem separable_x_pow_sub_c {n : ℕ} (a : F) (hn : (n : F) ≠ 0) (ha : a ≠ 0) :
-    Separable (x ^ n - c a) :=
+    Separable (X ^ n - C a) :=
   separable_x_pow_sub_c_unit (Units.mk0 a ha) (IsUnit.mk0 n hn)
 #align polynomial.separable_X_pow_sub_C Polynomial.separable_x_pow_sub_c
 
 -- this can possibly be strengthened to making `separable_X_pow_sub_C_unit` a
 -- bi-implication, but it is nontrivial!
 /-- In a field `F`, `X ^ n - 1` is separable iff `↑n ≠ 0`. -/
-theorem x_pow_sub_one_separable_iff {n : ℕ} : (x ^ n - 1 : F[X]).Separable ↔ (n : F) ≠ 0 :=
+theorem x_pow_sub_one_separable_iff {n : ℕ} : (X ^ n - 1 : F[X]).Separable ↔ (n : F) ≠ 0 :=
   by
   refine' ⟨_, fun h => separable_X_pow_sub_C_unit 1 (IsUnit.mk0 (↑n) h)⟩
   rw [separable_def', derivative_sub, derivative_X_pow, derivative_one, sub_zero]
@@ -439,7 +439,7 @@ variable {i : F →+* K}
 
 theorem eq_x_sub_c_of_separable_of_root_eq {x : F} {h : F[X]} (h_sep : h.Separable)
     (h_root : h.eval x = 0) (h_splits : Splits i h) (h_roots : ∀ y ∈ (h.map i).roots, y = i x) :
-    h = c (leadingCoeff h) * (x - c x) :=
+    h = C (leadingCoeff h) * (X - C x) :=
   by
   have h_ne_zero : h ≠ 0 := by
     rintro rfl
@@ -458,7 +458,7 @@ theorem eq_x_sub_c_of_separable_of_root_eq {x : F} {h : F[X]} (h_sep : h.Separab
 #align polynomial.eq_X_sub_C_of_separable_of_root_eq Polynomial.eq_x_sub_c_of_separable_of_root_eq
 
 theorem exists_finset_of_splits (i : F →+* K) {f : F[X]} (sep : Separable f) (sp : Splits i f) :
-    ∃ s : Finset K, f.map i = c (i f.leadingCoeff) * s.Prod fun a : K => x - c a :=
+    ∃ s : Finset K, f.map i = C (i f.leadingCoeff) * s.Prod fun a : K => X - C a :=
   by
   obtain ⟨s, h⟩ := (splits_iff_exists_multiset _).1 sp
   use s.to_finset

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

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

@@ -277,7 +277,7 @@ theorem separable_X_pow_sub_C_unit {n : ℕ} (u : Rˣ) (hn : IsUnit (n : R)) :
   calc
     -C ↑u⁻¹ * (X ^ n - C ↑u) + C ↑u⁻¹ * C n' * X * (↑n * X ^ (n - 1)) =
         C (↑u⁻¹ * ↑u) - C ↑u⁻¹ * X ^ n + C ↑u⁻¹ * C (n' * ↑n) * (X * X ^ (n - 1)) := by
-      simp only [C.map_mul, C_eq_nat_cast]
+      simp only [C.map_mul, C_eq_natCast]
       ring
     _ = 1 := by
       simp only [Units.inv_mul, hn', C.map_one, mul_one, ← pow_succ',

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

@@ -508,7 +508,7 @@ theorem eq_X_sub_C_of_separable_of_root_eq {x : F} {h : F[X]} (h_sep : h.Separab
     constructor
     · apply Finset.mem_mk.mpr
       · rw [mem_roots (show h.map i ≠ 0 from map_ne_zero h_ne_zero)]
-        rw [IsRoot.definition, ← eval₂_eq_eval_map, eval₂_hom, h_root]
+        rw [IsRoot.def, ← eval₂_eq_eval_map, eval₂_hom, h_root]
         exact RingHom.map_zero i
       · exact nodup_roots (Separable.map h_sep)
     · exact h_roots

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

@@ -3,9 +3,9 @@ Copyright (c) 2020 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
 -/
+import Mathlib.Algebra.Polynomial.Expand
+import Mathlib.Algebra.Polynomial.Splits
 import Mathlib.Algebra.Squarefree.Basic
-import Mathlib.Data.Polynomial.Expand
-import Mathlib.Data.Polynomial.Splits
 import Mathlib.FieldTheory.Minpoly.Field
 import Mathlib.RingTheory.PowerBasis
 

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

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

where the latter is more natural

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

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

but it seems to no longer apply.

Remarks on the PR :

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

@@ -120,7 +120,7 @@ theorem Separable.of_pow' {f : R[X]} :
   | 1 => fun h => Or.inr <| Or.inl ⟨pow_one f ▸ h, rfl⟩
   | n + 2 => fun h => by
     rw [pow_succ, pow_succ] at h
-    exact Or.inl (isCoprime_self.1 h.isCoprime.of_mul_right_left)
+    exact Or.inl (isCoprime_self.1 h.isCoprime.of_mul_left_right)
 #align polynomial.separable.of_pow' Polynomial.Separable.of_pow'
 
 theorem Separable.of_pow {f : R[X]} (hf : ¬IsUnit f) {n : ℕ} (hn : n ≠ 0)
@@ -280,7 +280,7 @@ theorem separable_X_pow_sub_C_unit {n : ℕ} (u : Rˣ) (hn : IsUnit (n : R)) :
       simp only [C.map_mul, C_eq_nat_cast]
       ring
     _ = 1 := by
-      simp only [Units.inv_mul, hn', C.map_one, mul_one, ← pow_succ,
+      simp only [Units.inv_mul, hn', C.map_one, mul_one, ← pow_succ',
         Nat.sub_add_cancel (show 1 ≤ n from hpos), sub_add_cancel]
 set_option linter.uppercaseLean3 false in
 #align polynomial.separable_X_pow_sub_C_unit Polynomial.separable_X_pow_sub_C_unit
@@ -400,7 +400,7 @@ theorem exists_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : p
       exact Nat.mul_lt_mul_of_pos_left hp.one_lt hg2.bot_lt
     rcases ih _ hg3 hg rfl with ⟨n, g, hg4, rfl⟩
     refine' ⟨n + 1, g, hg4, _⟩
-    rw [← hgf, expand_expand, pow_succ]
+    rw [← hgf, expand_expand, pow_succ']
 #align polynomial.exists_separable_of_irreducible Polynomial.exists_separable_of_irreducible
 
 theorem isUnit_or_eq_zero_of_separable_expand {f : F[X]} (n : ℕ) (hp : 0 < p)

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

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

@@ -508,7 +508,7 @@ theorem eq_X_sub_C_of_separable_of_root_eq {x : F} {h : F[X]} (h_sep : h.Separab
     constructor
     · apply Finset.mem_mk.mpr
       · rw [mem_roots (show h.map i ≠ 0 from map_ne_zero h_ne_zero)]
-        rw [IsRoot.def, ← eval₂_eq_eval_map, eval₂_hom, h_root]
+        rw [IsRoot.definition, ← eval₂_eq_eval_map, eval₂_hom, h_root]
         exact RingHom.map_zero i
       · exact nodup_roots (Separable.map h_sep)
     · exact h_roots

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)

@@ -674,9 +674,7 @@ end IsSeparableTower
 section CardAlgHom
 
 variable {R S T : Type*} [CommRing S]
-
 variable {K L F : Type*} [Field K] [Field L] [Field F]
-
 variable [Algebra K S] [Algebra K L]
 
 theorem AlgHom.card_of_powerBasis (pb : PowerBasis K S) (h_sep : (minpoly K pb.gen).Separable)

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

@@ -27,7 +27,8 @@ properties about separable polynomials here.
 
 universe u v w
 
-open Classical BigOperators Polynomial Finset
+open scoped Classical
+open BigOperators Polynomial Finset
 
 namespace Polynomial
 

... which states that if two polynomials are associated, then one is separable if and only if another one is. Also a separable polynomial multiplied by a unit is also separable.

@@ -134,6 +134,28 @@ theorem Separable.map {p : R[X]} (h : p.Separable) {f : R →+* S} : (p.map f).S
       Polynomial.map_one]⟩
 #align polynomial.separable.map Polynomial.Separable.map
 
+theorem _root_.Associated.separable {f g : R[X]}
+    (ha : Associated f g) (h : f.Separable) : g.Separable := by
+  obtain ⟨⟨u, v, h1, h2⟩, ha⟩ := ha
+  obtain ⟨a, b, h⟩ := h
+  refine ⟨a * v + b * derivative v, b * v, ?_⟩
+  replace h := congr($h * $(h1))
+  have h3 := congr(derivative $(h1))
+  simp only [← ha, derivative_mul, derivative_one] at h3 ⊢
+  calc
+    _ = (a * f + b * derivative f) * (u * v)
+      + (b * f) * (derivative u * v + u * derivative v) := by ring1
+    _ = 1 := by rw [h, h3]; ring1
+
+theorem _root_.Associated.separable_iff {f g : R[X]}
+    (ha : Associated f g) : f.Separable ↔ g.Separable := ⟨ha.separable, ha.symm.separable⟩
+
+theorem Separable.mul_unit {f g : R[X]} (hf : f.Separable) (hg : IsUnit g) : (f * g).Separable :=
+  (associated_mul_unit_right f g hg).separable hf
+
+theorem Separable.unit_mul {f g : R[X]} (hf : IsUnit f) (hg : g.Separable) : (f * g).Separable :=
+  (associated_unit_mul_right g f hf).separable hg
+
 theorem Separable.eval₂_derivative_ne_zero [Nontrivial S] (f : R →+* S) {p : R[X]}
     (h : p.Separable) {x : S} (hx : p.eval₂ f x = 0) :
     (derivative p).eval₂ f x ≠ 0 := by

Yet another small step toward Jordan-Chevalley-Dunford.

This was far more work than expected, partly because of missing API for Squarefree, and partly because the definition IsCoprime is the wrong concept for unique factorization domains.

@@ -3,7 +3,7 @@ Copyright (c) 2020 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
 -/
-import Mathlib.Algebra.Squarefree
+import Mathlib.Algebra.Squarefree.Basic
 import Mathlib.Data.Polynomial.Expand
 import Mathlib.Data.Polynomial.Splits
 import Mathlib.FieldTheory.Minpoly.Field
@@ -56,6 +56,7 @@ theorem not_separable_zero [Nontrivial R] : ¬Separable (0 : R[X]) := by
 theorem Separable.ne_zero [Nontrivial R] {f : R[X]} (h : f.Separable) : f ≠ 0 :=
   (not_separable_zero <| · ▸ h)
 
+@[simp]
 theorem separable_one : (1 : R[X]).Separable :=
   isCoprime_one_left
 #align polynomial.separable_one Polynomial.separable_one
@@ -173,6 +174,10 @@ theorem multiplicity_le_one_of_separable {p q : R[X]} (hq : ¬IsUnit q) (hsep :
   exact h
 #align polynomial.multiplicity_le_one_of_separable Polynomial.multiplicity_le_one_of_separable
 
+/-- A separable polynomial is square-free.
+
+See `PerfectField.separable_iff_squarefree` for the converse when the coefficients are a perfect
+field. -/
 theorem Separable.squarefree {p : R[X]} (hsep : Separable p) : Squarefree p := by
   rw [multiplicity.squarefree_iff_multiplicity_le_one p]
   exact fun f => or_iff_not_imp_right.mpr fun hunit => multiplicity_le_one_of_separable hunit hsep

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

From LeanAPAP

@@ -380,8 +380,7 @@ theorem isUnit_or_eq_zero_of_separable_expand {f : F[X]} (n : ℕ) (hp : 0 < p)
   rw [or_iff_not_imp_right]
   rintro hn : n ≠ 0
   have hf2 : derivative (expand F (p ^ n) f) = 0 := by
-    rw [derivative_expand, Nat.cast_pow, CharP.cast_eq_zero, zero_pow hn.bot_lt,
-      zero_mul, mul_zero]
+    rw [derivative_expand, Nat.cast_pow, CharP.cast_eq_zero, zero_pow hn, zero_mul, mul_zero]
   rw [separable_def, hf2, isCoprime_zero_right, isUnit_iff] at hf
   rcases hf with ⟨r, hr, hrf⟩
   rw [eq_comm, expand_eq_C (pow_pos hp _)] at hrf

@@ -635,8 +635,10 @@ lemma IsSeparable.of_equiv_equiv {A₁ B₁ A₂ B₂ : Type*} [Field A₁] [Fie
   letI := ((algebraMap A₁ B₁).comp e₁.symm.toRingHom).toAlgebra
   haveI : IsScalarTower A₁ A₂ B₁ := IsScalarTower.of_algebraMap_eq
     (fun x ↦ by simp [RingHom.algebraMap_toAlgebra])
-  let e : B₁ ≃ₐ[A₂] B₂ := { e₂ with commutes' := fun r ↦ by simpa [RingHom.algebraMap_toAlgebra]
-                                                  using DFunLike.congr_fun he.symm (e₁.symm r) }
+  let e : B₁ ≃ₐ[A₂] B₂ :=
+    { e₂ with
+      commutes' := fun r ↦ by
+        simpa [RingHom.algebraMap_toAlgebra] using DFunLike.congr_fun he.symm (e₁.symm r) }
   haveI := isSeparable_tower_top_of_isSeparable A₁ A₂ B₁
   exact IsSeparable.of_algHom _ _ e.symm.toAlgHom
 

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

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

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

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

@@ -636,7 +636,7 @@ lemma IsSeparable.of_equiv_equiv {A₁ B₁ A₂ B₂ : Type*} [Field A₁] [Fie
   haveI : IsScalarTower A₁ A₂ B₁ := IsScalarTower.of_algebraMap_eq
     (fun x ↦ by simp [RingHom.algebraMap_toAlgebra])
   let e : B₁ ≃ₐ[A₂] B₂ := { e₂ with commutes' := fun r ↦ by simpa [RingHom.algebraMap_toAlgebra]
-                                                  using FunLike.congr_fun he.symm (e₁.symm r) }
+                                                  using DFunLike.congr_fun he.symm (e₁.symm r) }
   haveI := isSeparable_tower_top_of_isSeparable A₁ A₂ B₁
   exact IsSeparable.of_algHom _ _ e.symm.toAlgHom
 

• nodup_[a]roots_iff_of_splits: a polynomial has no repeated roots if and only if it is separable.
• card_rootSet_eq_natDegree_iff_of_splits: a polynomial has number of roots equal to its degree if and only if it is separable. A converse to card_rootSet_eq_natDegree.

Also add some convenience lemmas:

• Separable.ne_zero: a separable polynomial is not zero.
• Separable.map_minpoly: if an element is separable over a small field, then it's also separable over a large field.

@@ -53,6 +53,9 @@ theorem not_separable_zero [Nontrivial R] : ¬Separable (0 : R[X]) := by
   simp only [derivative_zero, mul_zero, add_zero, zero_ne_one] at h
 #align polynomial.not_separable_zero Polynomial.not_separable_zero
 
+theorem Separable.ne_zero [Nontrivial R] {f : R[X]} (h : f.Separable) : f ≠ 0 :=
+  (not_separable_zero <| · ▸ h)
+
 theorem separable_one : (1 : R[X]).Separable :=
   isCoprime_one_left
 #align polynomial.separable_one Polynomial.separable_one
@@ -437,10 +440,32 @@ section Splits
 theorem card_rootSet_eq_natDegree [Algebra F K] {p : F[X]} (hsep : p.Separable)
     (hsplit : Splits (algebraMap F K) p) : Fintype.card (p.rootSet K) = p.natDegree := by
   simp_rw [rootSet_def, Finset.coe_sort_coe, Fintype.card_coe]
-  rw [Multiset.toFinset_card_of_nodup, ← natDegree_eq_card_roots hsplit]
-  exact nodup_roots hsep.map
+  rw [Multiset.toFinset_card_of_nodup (nodup_roots hsep.map), ← natDegree_eq_card_roots hsplit]
 #align polynomial.card_root_set_eq_nat_degree Polynomial.card_rootSet_eq_natDegree
 
+/-- If a non-zero polynomial splits, then it has no repeated roots on that field
+if and only if it is separable. -/
+theorem nodup_roots_iff_of_splits {f : F[X]} (hf : f ≠ 0) (h : f.Splits (RingHom.id F)) :
+    f.roots.Nodup ↔ f.Separable := by
+  refine ⟨(fun hnsep ↦ ?_).mtr, nodup_roots⟩
+  rw [Separable, ← gcd_isUnit_iff, isUnit_iff_degree_eq_zero] at hnsep
+  obtain ⟨x, hx⟩ := exists_root_of_splits _
+    (splits_of_splits_of_dvd _ hf h (gcd_dvd_left f _)) hnsep
+  simp_rw [Multiset.nodup_iff_count_le_one, not_forall, not_le]
+  exact ⟨x, ((one_lt_rootMultiplicity_iff_isRoot_gcd hf).2 hx).trans_eq f.count_roots.symm⟩
+
+/-- If a non-zero polynomial over `F` splits in `K`, then it has no repeated roots on `K`
+if and only if it is separable. -/
+theorem nodup_aroots_iff_of_splits [Algebra F K] {f : F[X]} (hf : f ≠ 0)
+    (h : f.Splits (algebraMap F K)) : (f.aroots K).Nodup ↔ f.Separable := by
+  rw [← (algebraMap F K).id_comp, ← splits_map_iff] at h
+  rw [nodup_roots_iff_of_splits (map_ne_zero hf) h, separable_map]
+
+theorem card_rootSet_eq_natDegree_iff_of_splits [Algebra F K] {f : F[X]} (hf : f ≠ 0)
+    (h : f.Splits (algebraMap F K)) : Fintype.card (f.rootSet K) = f.natDegree ↔ f.Separable := by
+  simp_rw [rootSet_def, Finset.coe_sort_coe, Fintype.card_coe, natDegree_eq_card_roots h,
+    Multiset.toFinset_card_eq_card_iff_nodup, nodup_aroots_iff_of_splits hf h]
+
 variable {i : F →+* K}
 
 theorem eq_X_sub_C_of_separable_of_root_eq {x : F} {h : F[X]} (h_sep : h.Separable)
@@ -528,7 +553,7 @@ theorem Polynomial.Separable.isIntegral {x : K} (h : (minpoly F x).Separable) :
   cases subsingleton_or_nontrivial F
   · haveI := Module.subsingleton F K
     exact ⟨1, monic_one, Subsingleton.elim _ _⟩
-  · exact of_not_not fun h' ↦ not_separable_zero (minpoly.eq_zero h' ▸ h)
+  · exact of_not_not (h.ne_zero <| minpoly.eq_zero ·)
 
 theorem IsSeparable.isIntegral [IsSeparable F K] :
     ∀ x : K, IsIntegral F x := fun x ↦ (IsSeparable.separable F x).isIntegral
@@ -571,11 +596,18 @@ instance (priority := 100) IsSeparable.of_finite (F K : Type*) [Field F] [Field
 
 section IsSeparableTower
 
+/-- If `R / K / A` is an extension tower, `x : R` is separable over `A`, then it's also separable
+over `K`. -/
+theorem Polynomial.Separable.map_minpoly {A : Type*} [CommRing A]
+    (K : Type*) [Field K] [Algebra A K] {R : Type*} [CommRing R] [Algebra A R] [Algebra K R]
+    [IsScalarTower A K R] {x : R} (h : (minpoly A x).Separable) : (minpoly K x).Separable :=
+  h.map.of_dvd (minpoly.dvd_map_of_isScalarTower _ _ _)
+
 variable (F K E : Type*) [Field F] [Field K] [Field E] [Algebra F K] [Algebra F E] [Algebra K E]
   [IsScalarTower F K E]
 
 theorem isSeparable_tower_top_of_isSeparable [IsSeparable F E] : IsSeparable K E :=
-  ⟨fun x ↦ (IsSeparable.separable F x).map.of_dvd (minpoly.dvd_map_of_isScalarTower _ _ _)⟩
+  ⟨fun x ↦ (IsSeparable.separable F x).map_minpoly _⟩
 #align is_separable_tower_top_of_is_separable isSeparable_tower_top_of_isSeparable
 
 theorem isSeparable_tower_bot_of_isSeparable [h : IsSeparable F E] : IsSeparable F K :=

@@ -595,6 +595,19 @@ theorem IsSeparable.of_algHom (E' : Type*) [Field E'] [Algebra F E'] (f : E →
   exact isSeparable_tower_bot_of_isSeparable F E E'
 #align is_separable.of_alg_hom IsSeparable.of_algHom
 
+lemma IsSeparable.of_equiv_equiv {A₁ B₁ A₂ B₂ : Type*} [Field A₁] [Field B₁]
+    [Field A₂] [Field B₂] [Algebra A₁ B₁] [Algebra A₂ B₂] (e₁ : A₁ ≃+* A₂) (e₂ : B₁ ≃+* B₂)
+    (he : RingHom.comp (algebraMap A₂ B₂) ↑e₁ = RingHom.comp ↑e₂ (algebraMap A₁ B₁))
+    [IsSeparable A₁ B₁] : IsSeparable A₂ B₂ := by
+  letI := e₁.toRingHom.toAlgebra
+  letI := ((algebraMap A₁ B₁).comp e₁.symm.toRingHom).toAlgebra
+  haveI : IsScalarTower A₁ A₂ B₁ := IsScalarTower.of_algebraMap_eq
+    (fun x ↦ by simp [RingHom.algebraMap_toAlgebra])
+  let e : B₁ ≃ₐ[A₂] B₂ := { e₂ with commutes' := fun r ↦ by simpa [RingHom.algebraMap_toAlgebra]
+                                                  using FunLike.congr_fun he.symm (e₁.symm r) }
+  haveI := isSeparable_tower_top_of_isSeparable A₁ A₂ B₁
+  exact IsSeparable.of_algHom _ _ e.symm.toAlgHom
+
 end IsSeparableTower
 
 section CardAlgHom

@@ -505,7 +505,7 @@ variable (F K : Type*) [CommRing F] [Ring K] [Algebra F K]
 -- to allow non-algebraic extensions, then the definition of `IsGalois` must also be changed.
 /-- Typeclass for separable field extension: `K` is a separable field extension of `F` iff
 the minimal polynomial of every `x : K` is separable. This implies that `K/F` is an algebraic
-extension, because the minimal polynomial of a non-integral element is 0, which is not
+extension, because the minimal polynomial of a non-integral element is `0`, which is not
 separable.
 
 We define this for general (commutative) rings and only assume `F` and `K` are fields if this
@@ -521,11 +521,17 @@ theorem IsSeparable.separable [IsSeparable F K] : ∀ x : K, (minpoly F x).Separ
   IsSeparable.separable'
 #align is_separable.separable IsSeparable.separable
 
-theorem IsSeparable.isIntegral [IsSeparable F K] : ∀ x : K, IsIntegral F x := fun x ↦ by
+variable {F} in
+/-- If the minimal polynomial of `x : K` over `F` is separable, then `x` is integral over `F`,
+because the minimal polynomial of a non-integral element is `0`, which is not separable. -/
+theorem Polynomial.Separable.isIntegral {x : K} (h : (minpoly F x).Separable) : IsIntegral F x := by
   cases subsingleton_or_nontrivial F
   · haveI := Module.subsingleton F K
     exact ⟨1, monic_one, Subsingleton.elim _ _⟩
-  · exact of_not_not fun h ↦ not_separable_zero (minpoly.eq_zero h ▸ IsSeparable.separable F x)
+  · exact of_not_not fun h' ↦ not_separable_zero (minpoly.eq_zero h' ▸ h)
+
+theorem IsSeparable.isIntegral [IsSeparable F K] :
+    ∀ x : K, IsIntegral F x := fun x ↦ (IsSeparable.separable F x).isIntegral
 #align is_separable.is_integral IsSeparable.isIntegral
 
 variable {F}

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

@@ -130,6 +130,19 @@ theorem Separable.map {p : R[X]} (h : p.Separable) {f : R →+* S} : (p.map f).S
       Polynomial.map_one]⟩
 #align polynomial.separable.map Polynomial.Separable.map
 
+theorem Separable.eval₂_derivative_ne_zero [Nontrivial S] (f : R →+* S) {p : R[X]}
+    (h : p.Separable) {x : S} (hx : p.eval₂ f x = 0) :
+    (derivative p).eval₂ f x ≠ 0 := by
+  intro hx'
+  obtain ⟨a, b, e⟩ := h
+  apply_fun Polynomial.eval₂ f x at e
+  simp only [eval₂_add, eval₂_mul, hx, mul_zero, hx', add_zero, eval₂_one, zero_ne_one] at e
+
+theorem Separable.aeval_derivative_ne_zero [Nontrivial S] [Algebra R S] {p : R[X]}
+    (h : p.Separable) {x : S} (hx : aeval x p = 0) :
+    aeval x (derivative p) ≠ 0 :=
+  h.eval₂_derivative_ne_zero (algebraMap R S) hx
+
 variable (p q : ℕ)
 
 theorem isUnit_of_self_mul_dvd_separable {p q : R[X]} (hp : p.Separable) (hq : q * q ∣ p) :

• add AlgEquiv.isSeparable, AlgEquiv.isSeparable_iff which states that IsSeparable is invariant under AlgEquiv
• also add IsSeparable.isAlgebraic which states that separable extension is algebraic

@@ -502,7 +502,7 @@ is needed for a proof.
   separable' (x : K) : (minpoly F x).Separable
 #align is_separable IsSeparable
 
-variable (F : Type*) {K : Type*} [CommRing F] [Ring K] [Algebra F K]
+variable {K}
 
 theorem IsSeparable.separable [IsSeparable F K] : ∀ x : K, (minpoly F x).Separable :=
   IsSeparable.separable'
@@ -515,12 +515,26 @@ theorem IsSeparable.isIntegral [IsSeparable F K] : ∀ x : K, IsIntegral F x :=
   · exact of_not_not fun h ↦ not_separable_zero (minpoly.eq_zero h ▸ IsSeparable.separable F x)
 #align is_separable.is_integral IsSeparable.isIntegral
 
-variable {F K : Type*} [CommRing F] [Ring K] [Algebra F K]
+variable {F}
 
 theorem isSeparable_iff : IsSeparable F K ↔ ∀ x : K, IsIntegral F x ∧ (minpoly F x).Separable :=
   ⟨fun _ x => ⟨IsSeparable.isIntegral F x, IsSeparable.separable F x⟩, fun h => ⟨fun x => (h x).2⟩⟩
 #align is_separable_iff isSeparable_iff
 
+variable {E : Type*} [Ring E] [Algebra F E] (e : K ≃ₐ[F] E)
+
+/-- Transfer `IsSeparable` across an `AlgEquiv`. -/
+theorem AlgEquiv.isSeparable [IsSeparable F K] : IsSeparable F E :=
+  ⟨fun _ ↦ by rw [← minpoly.algEquiv_eq e.symm]; exact IsSeparable.separable F _⟩
+
+theorem AlgEquiv.isSeparable_iff : IsSeparable F K ↔ IsSeparable F E :=
+  ⟨fun _ ↦ e.isSeparable, fun _ ↦ e.symm.isSeparable⟩
+
+variable (F K)
+
+theorem IsSeparable.isAlgebraic [Nontrivial F] [IsSeparable F K] : Algebra.IsAlgebraic F K :=
+  fun x ↦ (IsSeparable.isIntegral F x).isAlgebraic
+
 end CommRing
 
 instance isSeparable_self (F : Type*) [Field F] : IsSeparable F F :=

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

@@ -491,38 +491,40 @@ variable (F K : Type*) [CommRing F] [Ring K] [Algebra F K]
 -- is separable and normal, so if the definition of separable changes here at some point
 -- to allow non-algebraic extensions, then the definition of `IsGalois` must also be changed.
 /-- Typeclass for separable field extension: `K` is a separable field extension of `F` iff
-the minimal polynomial of every `x : K` is separable.
+the minimal polynomial of every `x : K` is separable. This implies that `K/F` is an algebraic
+extension, because the minimal polynomial of a non-integral element is 0, which is not
+separable.
 
 We define this for general (commutative) rings and only assume `F` and `K` are fields if this
 is needed for a proof.
 -/
-class IsSeparable : Prop where
-  isIntegral' (x : K) : IsIntegral F x
+@[mk_iff isSeparable_def] class IsSeparable : Prop where
   separable' (x : K) : (minpoly F x).Separable
 #align is_separable IsSeparable
 
 variable (F : Type*) {K : Type*} [CommRing F] [Ring K] [Algebra F K]
 
-theorem IsSeparable.isIntegral [IsSeparable F K] : ∀ x : K, IsIntegral F x :=
-  IsSeparable.isIntegral'
-#align is_separable.is_integral IsSeparable.isIntegral
-
 theorem IsSeparable.separable [IsSeparable F K] : ∀ x : K, (minpoly F x).Separable :=
   IsSeparable.separable'
 #align is_separable.separable IsSeparable.separable
 
+theorem IsSeparable.isIntegral [IsSeparable F K] : ∀ x : K, IsIntegral F x := fun x ↦ by
+  cases subsingleton_or_nontrivial F
+  · haveI := Module.subsingleton F K
+    exact ⟨1, monic_one, Subsingleton.elim _ _⟩
+  · exact of_not_not fun h ↦ not_separable_zero (minpoly.eq_zero h ▸ IsSeparable.separable F x)
+#align is_separable.is_integral IsSeparable.isIntegral
+
 variable {F K : Type*} [CommRing F] [Ring K] [Algebra F K]
 
 theorem isSeparable_iff : IsSeparable F K ↔ ∀ x : K, IsIntegral F x ∧ (minpoly F x).Separable :=
-  ⟨fun _ x => ⟨IsSeparable.isIntegral F x, IsSeparable.separable F x⟩, fun h =>
-    ⟨fun x => (h x).1, fun x => (h x).2⟩⟩
+  ⟨fun _ x => ⟨IsSeparable.isIntegral F x, IsSeparable.separable F x⟩, fun h => ⟨fun x => (h x).2⟩⟩
 #align is_separable_iff isSeparable_iff
 
 end CommRing
 
 instance isSeparable_self (F : Type*) [Field F] : IsSeparable F F :=
-  ⟨fun x => isIntegral_algebraMap,
-   fun x => by
+  ⟨fun x => by
     rw [minpoly.eq_X_sub_C']
     exact separable_X_sub_C⟩
 #align is_separable_self isSeparable_self
@@ -531,8 +533,7 @@ instance isSeparable_self (F : Type*) [Field F] : IsSeparable F F :=
 /-- A finite field extension in characteristic 0 is separable. -/
 instance (priority := 100) IsSeparable.of_finite (F K : Type*) [Field F] [Field K] [Algebra F K]
     [FiniteDimensional F K] [CharZero F] : IsSeparable F K :=
-  have : ∀ x : K, IsIntegral F x := fun _x ↦ .of_finite F _
-  ⟨this, fun x => (minpoly.irreducible (this x)).separable⟩
+  ⟨fun x => (minpoly.irreducible <| .of_finite F x).separable⟩
 #align is_separable.of_finite IsSeparable.of_finite
 
 section IsSeparableTower
@@ -541,18 +542,15 @@ variable (F K E : Type*) [Field F] [Field K] [Field E] [Algebra F K] [Algebra F
   [IsScalarTower F K E]
 
 theorem isSeparable_tower_top_of_isSeparable [IsSeparable F E] : IsSeparable K E :=
-  ⟨fun x ↦ (IsSeparable.isIntegral F x).tower_top, fun x ↦
-    (IsSeparable.separable F x).map.of_dvd (minpoly.dvd_map_of_isScalarTower _ _ _)⟩
+  ⟨fun x ↦ (IsSeparable.separable F x).map.of_dvd (minpoly.dvd_map_of_isScalarTower _ _ _)⟩
 #align is_separable_tower_top_of_is_separable isSeparable_tower_top_of_isSeparable
 
 theorem isSeparable_tower_bot_of_isSeparable [h : IsSeparable F E] : IsSeparable F K :=
-  isSeparable_iff.2 fun x ↦ by
-    refine (isSeparable_iff.1 h (algebraMap K E x)).imp .tower_bot_of_field fun hs ↦ ?_
-    obtain ⟨q, hq⟩ :=
+  ⟨fun x ↦
+    have ⟨_q, hq⟩ :=
       minpoly.dvd F x
         ((aeval_algebraMap_eq_zero_iff _ _ _).mp (minpoly.aeval F ((algebraMap K E) x)))
-    rw [hq] at hs
-    exact hs.of_mul_left
+    (hq ▸ h.separable (algebraMap K E x)).of_mul_left⟩
 #align is_separable_tower_bot_of_is_separable isSeparable_tower_bot_of_isSeparable
 
 variable {E}

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

@@ -283,9 +283,13 @@ theorem separable_iff_derivative_ne_zero {f : F[X]} (hf : Irreducible f) :
         natDegree_derivative_lt <| mt derivative_of_natDegree_zero h⟩
 #align polynomial.separable_iff_derivative_ne_zero Polynomial.separable_iff_derivative_ne_zero
 
-theorem separable_map (f : F →+* K) {p : F[X]} :
+attribute [local instance] Ideal.Quotient.field in
+theorem separable_map {S} [CommRing S] [Nontrivial S] (f : F →+* S) {p : F[X]} :
     (p.map f).Separable ↔ p.Separable := by
-  simp_rw [separable_def, derivative_map, isCoprime_map]
+  refine ⟨fun H ↦ ?_, fun H ↦ H.map⟩
+  obtain ⟨m, hm⟩ := Ideal.exists_maximal S
+  have := Separable.map H (f := Ideal.Quotient.mk m)
+  rwa [map_map, separable_def, derivative_map, isCoprime_map] at this
 #align polynomial.separable_map Polynomial.separable_map
 
 theorem separable_prod_X_sub_C_iff' {ι : Sort _} {f : ι → F} {s : Finset ι} :

Zulip

Initially I just wanted to add more dot notations for IsIntegral and IsAlgebraic (done in #8437); then I noticed near-duplicates Algebra.isIntegral_of_finite [Field R] [Ring A] and RingHom.IsIntegral.of_finite [CommRing R] [CommRing A] so I went on to generalize the latter to cover the former, and generalized everything in the IntegralClosure file to the noncommutative case whenever possible.

In the process I noticed more golfs, which result in this PR. Most notably, isIntegral_of_mem_of_FG is now proven using Cayley-Hamilton and doesn't depend on the Noetherian case isIntegral_of_noetherian; the latter is now proven using the former. In total the golfs makes mathlib 227 lines leaner (+487 -714).

The main changes are in the single file RingTheory/IntegralClosure:

• Change the definition of Algebra.IsIntegral which makes it unfold to IsIntegral rather than RingHom.IsIntegralElem because the former has much more APIs.

• Fix lemma names involving is_integral which are actually about IsIntegralElem: RingHom.is_integral_map → RingHom.isIntegralElem_map RingHom.is_integral_of_mem_closure → RingHom.IsIntegralElem.of_mem_closure RingHom.is_integral_zero/one → RingHom.isIntegralElem_zero/one RingHom.is_integral_add/neg/sub/mul/of_mul_unit → RingHom.IsIntegralElem.add/neg/sub/mul/of_mul_unit

• Add a lemma Algebra.IsIntegral.of_injective.

• Move isIntegral_of_(submodule_)noetherian down and golf them.

• Remove (Algebra.)isIntegral_of_finite that work only over fields, in favor of the more general (Algebra.)isIntegral.of_finite.

• Merge duplicate lemmas isIntegral_of_isScalarTower and isIntegral_tower_top_of_isIntegral into IsIntegral.tower_top.

• Golf IsIntegral.of_mem_of_fg by first proving IsIntegral.of_finite using Cayley-Hamilton.

• Add a docstring mentioning the Kurosh problem at Algebra.IsIntegral.finite. The negative solution to the problem means the theorem doesn't generalize to noncommutative algebras.

• Golf IsIntegral.tmul and isField_of_isIntegral_of_isField(').

• Combine isIntegral_trans_aux into isIntegral_trans and golf.

• Add Algebra namespace to isIntegral_sup.

• rename lemmas for dot notation: RingHom.isIntegral_trans → RingHom.IsIntegral.trans RingHom.isIntegral_quotient/tower_bot/top_of_isIntegral → RingHom.IsIntegral.quotient/tower_bot/top isIntegral_of_mem_closure' → IsIntegral.of_mem_closure' (and the '' version) isIntegral_of_surjective → Algebra.isIntegral_of_surjective

The next changed file is RingTheory/Algebraic:

• Rename: of_larger_base → tower_top (for consistency with IsIntegral) Algebra.isAlgebraic_of_finite → Algebra.IsAlgebraic.of_finite Algebra.isAlgebraic_trans → Algebra.IsAlgebraic.trans

• Add new lemmasAlgebra.IsIntegral.isAlgebraic, isAlgebraic_algHom_iff, and Algebra.IsAlgebraic.of_injective to streamline some proofs.

The generalization from CommRing to Ring requires an additional lemma scaleRoots_eval₂_mul_of_commute in Polynomial/ScaleRoots.

A lemma Algebra.lmul_injective is added to Algebra/Bilinear (in order to golf the proof of IsIntegral.of_mem_of_fg).

In all other files, I merely fix the changed names, or use newly available dot notations.

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

@@ -527,7 +527,7 @@ instance isSeparable_self (F : Type*) [Field F] : IsSeparable F F :=
 /-- A finite field extension in characteristic 0 is separable. -/
 instance (priority := 100) IsSeparable.of_finite (F K : Type*) [Field F] [Field K] [Algebra F K]
     [FiniteDimensional F K] [CharZero F] : IsSeparable F K :=
-  have : ∀ x : K, IsIntegral F x := fun _x => Algebra.isIntegral_of_finite _ _ _
+  have : ∀ x : K, IsIntegral F x := fun _x ↦ .of_finite F _
   ⟨this, fun x => (minpoly.irreducible (this x)).separable⟩
 #align is_separable.of_finite IsSeparable.of_finite
 
@@ -537,15 +537,13 @@ variable (F K E : Type*) [Field F] [Field K] [Field E] [Algebra F K] [Algebra F
   [IsScalarTower F K E]
 
 theorem isSeparable_tower_top_of_isSeparable [IsSeparable F E] : IsSeparable K E :=
-  ⟨fun x => isIntegral_of_isScalarTower (IsSeparable.isIntegral F x), fun x =>
+  ⟨fun x ↦ (IsSeparable.isIntegral F x).tower_top, fun x ↦
     (IsSeparable.separable F x).map.of_dvd (minpoly.dvd_map_of_isScalarTower _ _ _)⟩
 #align is_separable_tower_top_of_is_separable isSeparable_tower_top_of_isSeparable
 
 theorem isSeparable_tower_bot_of_isSeparable [h : IsSeparable F E] : IsSeparable F K :=
-  isSeparable_iff.2 fun x => by
-    refine'
-      (isSeparable_iff.1 h (algebraMap K E x)).imp IsIntegral.tower_bot_of_field
-        fun hs => _
+  isSeparable_iff.2 fun x ↦ by
+    refine (isSeparable_iff.1 h (algebraMap K E x)).imp .tower_bot_of_field fun hs ↦ ?_
     obtain ⟨q, hq⟩ :=
       minpoly.dvd F x
         ((aeval_algebraMap_eq_zero_iff _ _ _).mp (minpoly.aeval F ((algebraMap K E) x)))

This PR tests a string-based tool for renaming declarations.

Inspired by this Zulip thread, I am trying to reduce the diff of #8406.

This PR makes the following renames:

| From | To |

@@ -544,7 +544,7 @@ theorem isSeparable_tower_top_of_isSeparable [IsSeparable F E] : IsSeparable K E
 theorem isSeparable_tower_bot_of_isSeparable [h : IsSeparable F E] : IsSeparable F K :=
   isSeparable_iff.2 fun x => by
     refine'
-      (isSeparable_iff.1 h (algebraMap K E x)).imp isIntegral_tower_bot_of_isIntegral_field
+      (isSeparable_iff.1 h (algebraMap K E x)).imp IsIntegral.tower_bot_of_field
         fun hs => _
     obtain ⟨q, hq⟩ :=
       minpoly.dvd F x

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

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

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

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

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

@@ -59,7 +59,7 @@ theorem separable_one : (1 : R[X]).Separable :=
 
 @[nontriviality]
 theorem separable_of_subsingleton [Subsingleton R] (f : R[X]) : f.Separable := by
-  simp [Separable, IsCoprime]
+  simp [Separable, IsCoprime, eq_iff_true_of_subsingleton]
 #align polynomial.separable_of_subsingleton Polynomial.separable_of_subsingleton
 
 theorem separable_X_add_C (a : R) : (X + C a).Separable := by

This will improve spaces in the mathlib4 docs.

@@ -395,7 +395,7 @@ theorem unique_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : 0
 
 end CharP
 
-/-- If `n ≠ 0` in `F`, then ` X ^ n - a` is separable for any `a ≠ 0`. -/
+/-- If `n ≠ 0` in `F`, then `X ^ n - a` is separable for any `a ≠ 0`. -/
 theorem separable_X_pow_sub_C {n : ℕ} (a : F) (hn : (n : F) ≠ 0) (ha : a ≠ 0) :
     Separable (X ^ n - C a) :=
   separable_X_pow_sub_C_unit (Units.mk0 a ha) (IsUnit.mk0 (n : F) hn)

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

@@ -575,9 +575,8 @@ variable [Algebra K S] [Algebra K L]
 theorem AlgHom.card_of_powerBasis (pb : PowerBasis K S) (h_sep : (minpoly K pb.gen).Separable)
     (h_splits : (minpoly K pb.gen).Splits (algebraMap K L)) :
     @Fintype.card (S →ₐ[K] L) (PowerBasis.AlgHom.fintype pb) = pb.dim := by
-  let s := ((minpoly K pb.gen).map (algebraMap K L)).roots.toFinset
   let _ := (PowerBasis.AlgHom.fintype pb : Fintype (S →ₐ[K] L))
-  rw [Fintype.card_congr pb.liftEquiv', Fintype.card_of_subtype s (fun x => Multiset.mem_toFinset),
+  rw [Fintype.card_congr pb.liftEquiv', Fintype.card_of_subtype _ (fun x => Multiset.mem_toFinset),
     ← pb.natDegree_minpoly, natDegree_eq_card_roots h_splits, Multiset.toFinset_card_of_nodup]
   exact nodup_roots ((separable_map (algebraMap K L)).mpr h_sep)
 #align alg_hom.card_of_power_basis AlgHom.card_of_powerBasis

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).

@@ -345,7 +345,7 @@ theorem exists_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : p
     have hg1 : g.natDegree * p = N.succ := by rwa [← natDegree_expand, hgf]
     have hg2 : g.natDegree ≠ 0 := by
       intro this
-      rw [this, MulZeroClass.zero_mul] at hg1
+      rw [this, zero_mul] at hg1
       cases hg1
     have hg3 : g.natDegree < N.succ := by
       rw [← mul_one g.natDegree, ← hg1]
@@ -361,7 +361,7 @@ theorem isUnit_or_eq_zero_of_separable_expand {f : F[X]} (n : ℕ) (hp : 0 < p)
   rintro hn : n ≠ 0
   have hf2 : derivative (expand F (p ^ n) f) = 0 := by
     rw [derivative_expand, Nat.cast_pow, CharP.cast_eq_zero, zero_pow hn.bot_lt,
-      MulZeroClass.zero_mul, MulZeroClass.mul_zero]
+      zero_mul, mul_zero]
   rw [separable_def, hf2, isCoprime_zero_right, isUnit_iff] at hf
   rcases hf with ⟨r, hr, hrf⟩
   rw [eq_comm, expand_eq_C (pow_pos hp _)] at hrf
@@ -410,7 +410,7 @@ theorem X_pow_sub_one_separable_iff {n : ℕ} : (X ^ n - 1 : F[X]).Separable ↔
   rw [separable_def', derivative_sub, derivative_X_pow, derivative_one, sub_zero]
   -- Suppose `(n : F) = 0`, then the derivative is `0`, so `X ^ n - 1` is a unit, contradiction.
   rintro (h : IsCoprime _ _) hn'
-  rw [hn', C_0, MulZeroClass.zero_mul, isCoprime_zero_right] at h
+  rw [hn', C_0, zero_mul, isCoprime_zero_right] at h
   exact not_isUnit_X_pow_sub_one F n h
 set_option linter.uppercaseLean3 false in
 #align polynomial.X_pow_sub_one_separable_iff Polynomial.X_pow_sub_one_separable_iff

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

This has nice performance benefits.

@@ -94,12 +94,12 @@ theorem Separable.of_dvd {f g : R[X]} (hf : f.Separable) (hfg : g ∣ f) : g.Sep
   exact Separable.of_mul_left hf
 #align polynomial.separable.of_dvd Polynomial.Separable.of_dvd
 
-theorem separable_gcd_left {F : Type _} [Field F] {f : F[X]} (hf : f.Separable) (g : F[X]) :
+theorem separable_gcd_left {F : Type*} [Field F] {f : F[X]} (hf : f.Separable) (g : F[X]) :
     (EuclideanDomain.gcd f g).Separable :=
   Separable.of_dvd hf (EuclideanDomain.gcd_dvd_left f g)
 #align polynomial.separable_gcd_left Polynomial.separable_gcd_left
 
-theorem separable_gcd_right {F : Type _} [Field F] {g : F[X]} (f : F[X]) (hg : g.Separable) :
+theorem separable_gcd_right {F : Type*} [Field F] {g : F[X]} (f : F[X]) (hg : g.Separable) :
     (EuclideanDomain.gcd f g).Separable :=
   Separable.of_dvd hg (EuclideanDomain.gcd_dvd_right f g)
 #align polynomial.separable_gcd_right Polynomial.separable_gcd_right
@@ -479,7 +479,7 @@ open Polynomial
 
 section CommRing
 
-variable (F K : Type _) [CommRing F] [Ring K] [Algebra F K]
+variable (F K : Type*) [CommRing F] [Ring K] [Algebra F K]
 
 -- TODO: refactor to allow transcendental extensions?
 -- See: https://en.wikipedia.org/wiki/Separable_extension#Separability_of_transcendental_extensions
@@ -497,7 +497,7 @@ class IsSeparable : Prop where
   separable' (x : K) : (minpoly F x).Separable
 #align is_separable IsSeparable
 
-variable (F : Type _) {K : Type _} [CommRing F] [Ring K] [Algebra F K]
+variable (F : Type*) {K : Type*} [CommRing F] [Ring K] [Algebra F K]
 
 theorem IsSeparable.isIntegral [IsSeparable F K] : ∀ x : K, IsIntegral F x :=
   IsSeparable.isIntegral'
@@ -507,7 +507,7 @@ theorem IsSeparable.separable [IsSeparable F K] : ∀ x : K, (minpoly F x).Separ
   IsSeparable.separable'
 #align is_separable.separable IsSeparable.separable
 
-variable {F K : Type _} [CommRing F] [Ring K] [Algebra F K]
+variable {F K : Type*} [CommRing F] [Ring K] [Algebra F K]
 
 theorem isSeparable_iff : IsSeparable F K ↔ ∀ x : K, IsIntegral F x ∧ (minpoly F x).Separable :=
   ⟨fun _ x => ⟨IsSeparable.isIntegral F x, IsSeparable.separable F x⟩, fun h =>
@@ -516,7 +516,7 @@ theorem isSeparable_iff : IsSeparable F K ↔ ∀ x : K, IsIntegral F x ∧ (min
 
 end CommRing
 
-instance isSeparable_self (F : Type _) [Field F] : IsSeparable F F :=
+instance isSeparable_self (F : Type*) [Field F] : IsSeparable F F :=
   ⟨fun x => isIntegral_algebraMap,
    fun x => by
     rw [minpoly.eq_X_sub_C']
@@ -525,7 +525,7 @@ instance isSeparable_self (F : Type _) [Field F] : IsSeparable F F :=
 
 -- See note [lower instance priority]
 /-- A finite field extension in characteristic 0 is separable. -/
-instance (priority := 100) IsSeparable.of_finite (F K : Type _) [Field F] [Field K] [Algebra F K]
+instance (priority := 100) IsSeparable.of_finite (F K : Type*) [Field F] [Field K] [Algebra F K]
     [FiniteDimensional F K] [CharZero F] : IsSeparable F K :=
   have : ∀ x : K, IsIntegral F x := fun _x => Algebra.isIntegral_of_finite _ _ _
   ⟨this, fun x => (minpoly.irreducible (this x)).separable⟩
@@ -533,7 +533,7 @@ instance (priority := 100) IsSeparable.of_finite (F K : Type _) [Field F] [Field
 
 section IsSeparableTower
 
-variable (F K E : Type _) [Field F] [Field K] [Field E] [Algebra F K] [Algebra F E] [Algebra K E]
+variable (F K E : Type*) [Field F] [Field K] [Field E] [Algebra F K] [Algebra F E] [Algebra K E]
   [IsScalarTower F K E]
 
 theorem isSeparable_tower_top_of_isSeparable [IsSeparable F E] : IsSeparable K E :=
@@ -555,7 +555,7 @@ theorem isSeparable_tower_bot_of_isSeparable [h : IsSeparable F E] : IsSeparable
 
 variable {E}
 
-theorem IsSeparable.of_algHom (E' : Type _) [Field E'] [Algebra F E'] (f : E →ₐ[F] E')
+theorem IsSeparable.of_algHom (E' : Type*) [Field E'] [Algebra F E'] (f : E →ₐ[F] E')
     [IsSeparable F E'] : IsSeparable F E := by
   letI : Algebra E E' := RingHom.toAlgebra f.toRingHom
   haveI : IsScalarTower F E E' := IsScalarTower.of_algebraMap_eq fun x => (f.commutes x).symm
@@ -566,9 +566,9 @@ end IsSeparableTower
 
 section CardAlgHom
 
-variable {R S T : Type _} [CommRing S]
+variable {R S T : Type*} [CommRing S]
 
-variable {K L F : Type _} [Field K] [Field L] [Field F]
+variable {K L F : Type*} [Field K] [Field L] [Field F]
 
 variable [Algebra K S] [Algebra K L]
 

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
-
-! This file was ported from Lean 3 source module field_theory.separable
-! leanprover-community/mathlib commit 92ca63f0fb391a9ca5f22d2409a6080e786d99f7
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Squarefree
 import Mathlib.Data.Polynomial.Expand
@@ -14,6 +9,8 @@ import Mathlib.Data.Polynomial.Splits
 import Mathlib.FieldTheory.Minpoly.Field
 import Mathlib.RingTheory.PowerBasis
 
+#align_import field_theory.separable from "leanprover-community/mathlib"@"92ca63f0fb391a9ca5f22d2409a6080e786d99f7"
+
 /-!
 
 # Separable polynomials

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -333,7 +333,7 @@ theorem separable_or {f : F[X]} (hf : Irreducible f) :
 #align polynomial.separable_or Polynomial.separable_or
 
 theorem exists_separable_of_irreducible {f : F[X]} (hf : Irreducible f) (hp : p ≠ 0) :
-    ∃ (n : ℕ)(g : F[X]), g.Separable ∧ expand F (p ^ n) g = f := by
+    ∃ (n : ℕ) (g : F[X]), g.Separable ∧ expand F (p ^ n) g = f := by
   replace hp : p.Prime := (CharP.char_is_prime_or_zero F p).resolve_right hp
   induction' hn : f.natDegree using Nat.strong_induction_on with N ih generalizing f
   rcases separable_or p hf with (h | ⟨h1, g, hg, hgf⟩)

@@ -30,9 +30,7 @@ properties about separable polynomials here.
 
 universe u v w
 
-open Classical BigOperators Polynomial
-
-open Finset
+open Classical BigOperators Polynomial Finset
 
 namespace Polynomial
 
@@ -164,10 +162,7 @@ theorem multiplicity_le_one_of_separable {p q : R[X]} (hq : ¬IsUnit q) (hsep :
 
 theorem Separable.squarefree {p : R[X]} (hsep : Separable p) : Squarefree p := by
   rw [multiplicity.squarefree_iff_multiplicity_le_one p]
-  intro f
-  by_cases hunit : IsUnit f
-  · exact Or.inr hunit
-  exact Or.inl (multiplicity_le_one_of_separable hunit hsep)
+  exact fun f => or_iff_not_imp_right.mpr fun hunit => multiplicity_le_one_of_separable hunit hsep
 #align polynomial.separable.squarefree Polynomial.Separable.squarefree
 
 end CommSemiring
@@ -491,9 +486,9 @@ variable (F K : Type _) [CommRing F] [Ring K] [Algebra F K]
 
 -- TODO: refactor to allow transcendental extensions?
 -- See: https://en.wikipedia.org/wiki/Separable_extension#Separability_of_transcendental_extensions
--- Note that right now a Galois extension (class `is_galois`) is defined to be an extension which
+-- Note that right now a Galois extension (class `IsGalois`) is defined to be an extension which
 -- is separable and normal, so if the definition of separable changes here at some point
--- to allow non-algebraic extensions, then the definition of `is_galois` must also be changed.
+-- to allow non-algebraic extensions, then the definition of `IsGalois` must also be changed.
 /-- Typeclass for separable field extension: `K` is a separable field extension of `F` iff
 the minimal polynomial of every `x : K` is separable.
 
@@ -501,14 +496,14 @@ We define this for general (commutative) rings and only assume `F` and `K` are f
 is needed for a proof.
 -/
 class IsSeparable : Prop where
-  is_integral' (x : K) : IsIntegral F x
+  isIntegral' (x : K) : IsIntegral F x
   separable' (x : K) : (minpoly F x).Separable
 #align is_separable IsSeparable
 
 variable (F : Type _) {K : Type _} [CommRing F] [Ring K] [Algebra F K]
 
 theorem IsSeparable.isIntegral [IsSeparable F K] : ∀ x : K, IsIntegral F x :=
-  IsSeparable.is_integral'
+  IsSeparable.isIntegral'
 #align is_separable.is_integral IsSeparable.isIntegral
 
 theorem IsSeparable.separable [IsSeparable F K] : ∀ x : K, (minpoly F x).Separable :=
@@ -525,7 +520,8 @@ theorem isSeparable_iff : IsSeparable F K ↔ ∀ x : K, IsIntegral F x ∧ (min
 end CommRing
 
 instance isSeparable_self (F : Type _) [Field F] : IsSeparable F F :=
-  ⟨fun x => isIntegral_algebraMap, fun x => by
+  ⟨fun x => isIntegral_algebraMap,
+   fun x => by
     rw [minpoly.eq_X_sub_C']
     exact separable_X_sub_C⟩
 #align is_separable_self isSeparable_self