ring_theory.algebraic ⟷ Mathlib.RingTheory.Algebraic

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

@@ -5,7 +5,7 @@ Authors: Johan Commelin
 -/
 import LinearAlgebra.FiniteDimensional
 import RingTheory.IntegralClosure
-import Data.Polynomial.IntegralNormalization
+import RingTheory.Polynomial.IntegralNormalization
 
 #align_import ring_theory.algebraic from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
 
@@ -370,7 +370,7 @@ end Algebra
 
 variable {R S : Type _} [CommRing R] [IsDomain R] [CommRing S]
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (y «expr ≠ » (0 : R)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (y «expr ≠ » (0 : R)) -/
 #print exists_integral_multiple /-
 theorem exists_integral_multiple [Algebra R S] {z : S} (hz : IsAlgebraic R z)
     (inj : ∀ x, algebraMap R S x = 0 → x = 0) :
@@ -387,7 +387,7 @@ theorem exists_integral_multiple [Algebra R S] {z : S} (hz : IsAlgebraic R z)
 #align exists_integral_multiple exists_integral_multiple
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (d «expr ≠ » (0 : R)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (d «expr ≠ » (0 : R)) -/
 #print IsIntegralClosure.exists_smul_eq_mul /-
 /-- A fraction `(a : S) / (b : S)` can be reduced to `(c : S) / (d : R)`,
 if `S` is the integral closure of `R` in an algebraic extension `L` of `R`. -/
@@ -403,7 +403,7 @@ theorem IsIntegralClosure.exists_smul_eq_mul {L : Type _} [Field L] [Algebra R S
     ⟨IsIntegralClosure.mk' S (c : L) c.2, d, d_ne, IsIntegralClosure.algebraMap_injective S R L _⟩
   simp only [Algebra.smul_def, RingHom.map_mul, IsIntegralClosure.algebraMap_mk', ← hx, ←
     IsScalarTower.algebraMap_apply]
-  rw [← mul_assoc _ (_ / _), mul_div_cancel' (algebraMap S L a), mul_comm]
+  rw [← mul_assoc _ (_ / _), mul_div_cancel₀ (algebraMap S L a), mul_comm]
   exact mt ((injective_iff_map_eq_zero _).mp (IsIntegralClosure.algebraMap_injective S R L) _) hb
 #align is_integral_closure.exists_smul_eq_mul IsIntegralClosure.exists_smul_eq_mul
 -/

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

@@ -452,7 +452,7 @@ theorem Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero {x : A} {p : K[X]}
 theorem Subalgebra.inv_mem_of_algebraic {x : A} (hx : IsAlgebraic K (x : L)) : (x⁻¹ : L) ∈ A :=
   by
   obtain ⟨p, ne_zero, aeval_eq⟩ := hx
-  rw [Subalgebra.aeval_coe, Subalgebra.coe_eq_zero] at aeval_eq 
+  rw [Subalgebra.aeval_coe, Subalgebra.coe_eq_zero] at aeval_eq
   revert ne_zero aeval_eq
   refine' p.rec_on_horner _ _ _
   · intro h
@@ -461,7 +461,7 @@ theorem Subalgebra.inv_mem_of_algebraic {x : A} (hx : IsAlgebraic K (x : L)) : (
     refine' A.inv_mem_of_root_of_coeff_zero_ne_zero aeval_eq _
     rwa [coeff_add, hp, zero_add, coeff_C, if_pos rfl]
   · intro p hp ih ne_zero aeval_eq
-    rw [AlgHom.map_mul, aeval_X, mul_eq_zero] at aeval_eq 
+    rw [AlgHom.map_mul, aeval_X, mul_eq_zero] at aeval_eq
     cases' aeval_eq with aeval_eq x_eq
     · exact ih hp aeval_eq
     · rw [x_eq, Subalgebra.coe_zero, inv_zero]

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

@@ -168,28 +168,27 @@ theorem isAlgebraic_of_mem_rootSet {R : Type u} {A : Type v} [Field R] [Field A]
 
 open IsScalarTower
 
-#print isAlgebraic_algebraMap_of_isAlgebraic /-
-theorem isAlgebraic_algebraMap_of_isAlgebraic {a : S} :
-    IsAlgebraic R a → IsAlgebraic R (algebraMap S A a) := fun ⟨f, hf₁, hf₂⟩ =>
-  ⟨f, hf₁, by rw [aeval_algebra_map_apply, hf₂, map_zero]⟩
-#align is_algebraic_algebra_map_of_is_algebraic isAlgebraic_algebraMap_of_isAlgebraic
+#print IsAlgebraic.algebraMap /-
+theorem IsAlgebraic.algebraMap {a : S} : IsAlgebraic R a → IsAlgebraic R (algebraMap S A a) :=
+  fun ⟨f, hf₁, hf₂⟩ => ⟨f, hf₁, by rw [aeval_algebra_map_apply, hf₂, map_zero]⟩
+#align is_algebraic_algebra_map_of_is_algebraic IsAlgebraic.algebraMap
 -/
 
-#print isAlgebraic_algHom_of_isAlgebraic /-
+#print IsAlgebraic.algHom /-
 /-- This is slightly more general than `is_algebraic_algebra_map_of_is_algebraic` in that it
   allows noncommutative intermediate rings `A`. -/
-theorem isAlgebraic_algHom_of_isAlgebraic {B} [Ring B] [Algebra R B] (f : A →ₐ[R] B) {a : A}
+theorem IsAlgebraic.algHom {B} [Ring B] [Algebra R B] (f : A →ₐ[R] B) {a : A}
     (h : IsAlgebraic R a) : IsAlgebraic R (f a) :=
   let ⟨p, hp, ha⟩ := h
   ⟨p, hp, by rw [aeval_alg_hom, f.comp_apply, ha, map_zero]⟩
-#align is_algebraic_alg_hom_of_is_algebraic isAlgebraic_algHom_of_isAlgebraic
+#align is_algebraic_alg_hom_of_is_algebraic IsAlgebraic.algHom
 -/
 
 #print AlgEquiv.isAlgebraic /-
 /-- Transfer `algebra.is_algebraic` across an `alg_equiv`. -/
 theorem AlgEquiv.isAlgebraic {B} [Ring B] [Algebra R B] (e : A ≃ₐ[R] B)
     (h : Algebra.IsAlgebraic R A) : Algebra.IsAlgebraic R B := fun b => by
-  convert ← isAlgebraic_algHom_of_isAlgebraic e.to_alg_hom (h _) <;> apply e.apply_symm_apply
+  convert ← IsAlgebraic.algHom e.to_alg_hom (h _) <;> apply e.apply_symm_apply
 #align alg_equiv.is_algebraic AlgEquiv.isAlgebraic
 -/
 
@@ -204,23 +203,23 @@ theorem AlgEquiv.isAlgebraic_iff {B} [Ring B] [Algebra R B] (e : A ≃ₐ[R] B)
 theorem isAlgebraic_algebraMap_iff {a : S} (h : Function.Injective (algebraMap S A)) :
     IsAlgebraic R (algebraMap S A a) ↔ IsAlgebraic R a :=
   ⟨fun ⟨p, hp0, hp⟩ => ⟨p, hp0, h (by rwa [map_zero, ← aeval_algebra_map_apply])⟩,
-    isAlgebraic_algebraMap_of_isAlgebraic⟩
+    IsAlgebraic.algebraMap⟩
 #align is_algebraic_algebra_map_iff isAlgebraic_algebraMap_iff
 -/
 
-#print isAlgebraic_of_pow /-
-theorem isAlgebraic_of_pow {r : A} {n : ℕ} (hn : 0 < n) (ht : IsAlgebraic R (r ^ n)) :
+#print IsAlgebraic.of_pow /-
+theorem IsAlgebraic.of_pow {r : A} {n : ℕ} (hn : 0 < n) (ht : IsAlgebraic R (r ^ n)) :
     IsAlgebraic R r := by
   obtain ⟨p, p_nonzero, hp⟩ := ht
   refine' ⟨Polynomial.expand _ n p, _, _⟩
   · rwa [Polynomial.expand_ne_zero hn]
   · rwa [Polynomial.expand_aeval n p r]
-#align is_algebraic_of_pow isAlgebraic_of_pow
+#align is_algebraic_of_pow IsAlgebraic.of_pow
 -/
 
 #print Transcendental.pow /-
 theorem Transcendental.pow {r : A} (ht : Transcendental R r) {n : ℕ} (hn : 0 < n) :
-    Transcendental R (r ^ n) := fun ht' => ht <| isAlgebraic_of_pow hn ht'
+    Transcendental R (r ^ n) := fun ht' => ht <| IsAlgebraic.of_pow hn ht'
 #align transcendental.pow Transcendental.pow
 -/
 
@@ -260,66 +259,65 @@ variable [Algebra K L] [Algebra L A] [Algebra K A] [IsScalarTower K L A]
 
 variable [Algebra R S] [Algebra S A] [Algebra R A] [IsScalarTower R S A]
 
-#print Algebra.isAlgebraic_trans /-
+#print Algebra.IsAlgebraic.trans /-
 /-- If L is an algebraic field extension of K and A is an algebraic algebra over L,
 then A is algebraic over K. -/
-theorem isAlgebraic_trans (L_alg : IsAlgebraic K L) (A_alg : IsAlgebraic L A) : IsAlgebraic K A :=
+theorem Algebra.IsAlgebraic.trans (L_alg : IsAlgebraic K L) (A_alg : IsAlgebraic L A) :
+    IsAlgebraic K A :=
   by
   simp only [IsAlgebraic, isAlgebraic_iff_isIntegral] at L_alg A_alg ⊢
   exact isIntegral_trans L_alg A_alg
-#align algebra.is_algebraic_trans Algebra.isAlgebraic_trans
+#align algebra.is_algebraic_trans Algebra.IsAlgebraic.trans
 -/
 
 variable (K L)
 
-#print isAlgebraic_of_larger_base_of_injective /-
+#print IsAlgebraic.tower_top_of_injective /-
 /-- If x is algebraic over R, then x is algebraic over S when S is an extension of R,
   and the map from `R` to `S` is injective. -/
-theorem isAlgebraic_of_larger_base_of_injective (hinj : Function.Injective (algebraMap R S)) {x : A}
+theorem IsAlgebraic.tower_top_of_injective (hinj : Function.Injective (algebraMap R S)) {x : A}
     (A_alg : IsAlgebraic R x) : IsAlgebraic S x :=
   let ⟨p, hp₁, hp₂⟩ := A_alg
   ⟨p.map (algebraMap _ _), by
     rwa [Ne.def, ← degree_eq_bot, degree_map_eq_of_injective hinj, degree_eq_bot], by simpa⟩
-#align is_algebraic_of_larger_base_of_injective isAlgebraic_of_larger_base_of_injective
+#align is_algebraic_of_larger_base_of_injective IsAlgebraic.tower_top_of_injective
 -/
 
-#print Algebra.isAlgebraic_of_larger_base_of_injective /-
+#print Algebra.IsAlgebraic.tower_top_of_injective /-
 /-- If A is an algebraic algebra over R, then A is algebraic over S when S is an extension of R,
   and the map from `R` to `S` is injective. -/
-theorem isAlgebraic_of_larger_base_of_injective (hinj : Function.Injective (algebraMap R S))
+theorem Algebra.IsAlgebraic.tower_top_of_injective (hinj : Function.Injective (algebraMap R S))
     (A_alg : IsAlgebraic R A) : IsAlgebraic S A := fun x =>
-  isAlgebraic_of_larger_base_of_injective hinj (A_alg x)
-#align algebra.is_algebraic_of_larger_base_of_injective Algebra.isAlgebraic_of_larger_base_of_injective
+  IsAlgebraic.tower_top_of_injective hinj (A_alg x)
+#align algebra.is_algebraic_of_larger_base_of_injective Algebra.IsAlgebraic.tower_top_of_injective
 -/
 
-#print isAlgebraic_of_larger_base /-
+#print IsAlgebraic.tower_top /-
 /-- If x is a algebraic over K, then x is algebraic over L when L is an extension of K -/
-theorem isAlgebraic_of_larger_base {x : A} (A_alg : IsAlgebraic K x) : IsAlgebraic L x :=
-  isAlgebraic_of_larger_base_of_injective (algebraMap K L).Injective A_alg
-#align is_algebraic_of_larger_base isAlgebraic_of_larger_base
+theorem IsAlgebraic.tower_top {x : A} (A_alg : IsAlgebraic K x) : IsAlgebraic L x :=
+  IsAlgebraic.tower_top_of_injective (algebraMap K L).Injective A_alg
+#align is_algebraic_of_larger_base IsAlgebraic.tower_top
 -/
 
-#print Algebra.isAlgebraic_of_larger_base /-
+#print Algebra.IsAlgebraic.tower_top /-
 /-- If A is an algebraic algebra over K, then A is algebraic over L when L is an extension of K -/
-theorem isAlgebraic_of_larger_base (A_alg : IsAlgebraic K A) : IsAlgebraic L A :=
-  isAlgebraic_of_larger_base_of_injective (algebraMap K L).Injective A_alg
-#align algebra.is_algebraic_of_larger_base Algebra.isAlgebraic_of_larger_base
+theorem Algebra.IsAlgebraic.tower_top (A_alg : IsAlgebraic K A) : IsAlgebraic L A :=
+  Algebra.IsAlgebraic.tower_top_of_injective (algebraMap K L).Injective A_alg
+#align algebra.is_algebraic_of_larger_base Algebra.IsAlgebraic.tower_top
 -/
 
 variable (K L)
 
-#print Algebra.isIntegral_of_finite /-
 /-- A field extension is integral if it is finite. -/
 theorem isIntegral_of_finite [FiniteDimensional K L] : Algebra.IsIntegral K L := fun x =>
   isIntegral_of_submodule_noetherian ⊤ (IsNoetherian.iff_fg.2 inferInstance) x Algebra.mem_top
 #align algebra.is_integral_of_finite Algebra.isIntegral_of_finite
--/
 
-#print Algebra.isAlgebraic_of_finite /-
+#print Algebra.IsAlgebraic.of_finite /-
 /-- A field extension is algebraic if it is finite. -/
-theorem isAlgebraic_of_finite [finite : FiniteDimensional K L] : IsAlgebraic K L :=
+theorem Algebra.IsAlgebraic.of_finite [finite : FiniteDimensional K L] : IsAlgebraic K L :=
   Algebra.isAlgebraic_iff_isIntegral.mpr (isIntegral_of_finite K L)
-#align algebra.is_algebraic_of_finite Algebra.isAlgebraic_of_finite
+#align algebra.is_algebraic_of_finite Algebra.IsAlgebraic.of_finite
 -/
 
 variable {K L}
@@ -341,7 +339,7 @@ theorem IsAlgebraic.algHom_bijective (ha : Algebra.IsAlgebraic K L) (f : L →
 
 #print AlgHom.bijective /-
 theorem AlgHom.bijective [FiniteDimensional K L] (ϕ : L →ₐ[K] L) : Function.Bijective ϕ :=
-  (Algebra.isAlgebraic_of_finite K L).algHom_bijective ϕ
+  (Algebra.IsAlgebraic.of_finite K L).algHom_bijective ϕ
 #align alg_hom.bijective AlgHom.bijective
 -/
 
@@ -364,7 +362,7 @@ noncomputable def IsAlgebraic.algEquivEquivAlgHom (ha : Algebra.IsAlgebraic K L)
 /-- Bijection between algebra equivalences and algebra homomorphisms -/
 @[reducible]
 noncomputable def algEquivEquivAlgHom [FiniteDimensional K L] : (L ≃ₐ[K] L) ≃* (L →ₐ[K] L) :=
-  (Algebra.isAlgebraic_of_finite K L).algEquivEquivAlgHom K L
+  (Algebra.IsAlgebraic.of_finite K L).algEquivEquivAlgHom K L
 #align alg_equiv_equiv_alg_hom algEquivEquivAlgHom
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010

@@ -99,7 +99,7 @@ theorem Algebra.isAlgebraic_iff : Algebra.IsAlgebraic R A ↔ (⊤ : Subalgebra
 #print isAlgebraic_iff_not_injective /-
 theorem isAlgebraic_iff_not_injective {x : A} :
     IsAlgebraic R x ↔ ¬Function.Injective (Polynomial.aeval x : R[X] →ₐ[R] A) := by
-  simp only [IsAlgebraic, injective_iff_map_eq_zero, not_forall, and_comm, exists_prop]
+  simp only [IsAlgebraic, injective_iff_map_eq_zero, Classical.not_forall, and_comm, exists_prop]
 #align is_algebraic_iff_not_injective isAlgebraic_iff_not_injective
 -/
 

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

@@ -3,9 +3,9 @@ Copyright (c) 2019 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 -/
-import Mathbin.LinearAlgebra.FiniteDimensional
-import Mathbin.RingTheory.IntegralClosure
-import Mathbin.Data.Polynomial.IntegralNormalization
+import LinearAlgebra.FiniteDimensional
+import RingTheory.IntegralClosure
+import Data.Polynomial.IntegralNormalization
 
 #align_import ring_theory.algebraic from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
 
@@ -372,7 +372,7 @@ end Algebra
 
 variable {R S : Type _} [CommRing R] [IsDomain R] [CommRing S]
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y «expr ≠ » (0 : R)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (y «expr ≠ » (0 : R)) -/
 #print exists_integral_multiple /-
 theorem exists_integral_multiple [Algebra R S] {z : S} (hz : IsAlgebraic R z)
     (inj : ∀ x, algebraMap R S x = 0 → x = 0) :
@@ -389,7 +389,7 @@ theorem exists_integral_multiple [Algebra R S] {z : S} (hz : IsAlgebraic R z)
 #align exists_integral_multiple exists_integral_multiple
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (d «expr ≠ » (0 : R)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (d «expr ≠ » (0 : R)) -/
 #print IsIntegralClosure.exists_smul_eq_mul /-
 /-- A fraction `(a : S) / (b : S)` can be reduced to `(c : S) / (d : R)`,
 if `S` is the integral closure of `R` in an algebraic extension `L` of `R`. -/

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

@@ -2,16 +2,13 @@
 Copyright (c) 2019 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
-
-! This file was ported from Lean 3 source module ring_theory.algebraic
-! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.FiniteDimensional
 import Mathbin.RingTheory.IntegralClosure
 import Mathbin.Data.Polynomial.IntegralNormalization
 
+#align_import ring_theory.algebraic from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
+
 /-!
 # Algebraic elements and algebraic extensions
 
@@ -375,7 +372,7 @@ end Algebra
 
 variable {R S : Type _} [CommRing R] [IsDomain R] [CommRing S]
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (y «expr ≠ » (0 : R)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y «expr ≠ » (0 : R)) -/
 #print exists_integral_multiple /-
 theorem exists_integral_multiple [Algebra R S] {z : S} (hz : IsAlgebraic R z)
     (inj : ∀ x, algebraMap R S x = 0 → x = 0) :
@@ -392,7 +389,7 @@ theorem exists_integral_multiple [Algebra R S] {z : S} (hz : IsAlgebraic R z)
 #align exists_integral_multiple exists_integral_multiple
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (d «expr ≠ » (0 : R)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (d «expr ≠ » (0 : R)) -/
 #print IsIntegralClosure.exists_smul_eq_mul /-
 /-- A fraction `(a : S) / (b : S)` can be reduced to `(c : S) / (d : R)`,
 if `S` is the integral closure of `R` in an algebraic extension `L` of `R`. -/

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

@@ -76,6 +76,7 @@ def Algebra.IsAlgebraic : Prop :=
 
 variable {R A}
 
+#print Subalgebra.isAlgebraic_iff /-
 /-- A subalgebra is algebraic if and only if it is algebraic as an algebra. -/
 theorem Subalgebra.isAlgebraic_iff (S : Subalgebra R A) :
     S.IsAlgebraic ↔ @Algebra.IsAlgebraic R S _ _ S.Algebra :=
@@ -87,18 +88,23 @@ theorem Subalgebra.isAlgebraic_iff (S : Subalgebra R A) :
   conv_rhs => rw [← h.eq_iff, AlgHom.map_zero]
   rw [← aeval_alg_hom_apply, S.val_apply]
 #align subalgebra.is_algebraic_iff Subalgebra.isAlgebraic_iff
+-/
 
+#print Algebra.isAlgebraic_iff /-
 /-- An algebra is algebraic if and only if it is algebraic as a subalgebra. -/
 theorem Algebra.isAlgebraic_iff : Algebra.IsAlgebraic R A ↔ (⊤ : Subalgebra R A).IsAlgebraic :=
   by
   delta Algebra.IsAlgebraic Subalgebra.IsAlgebraic
   simp only [Algebra.mem_top, forall_prop_of_true, iff_self_iff]
 #align algebra.is_algebraic_iff Algebra.isAlgebraic_iff
+-/
 
+#print isAlgebraic_iff_not_injective /-
 theorem isAlgebraic_iff_not_injective {x : A} :
     IsAlgebraic R x ↔ ¬Function.Injective (Polynomial.aeval x : R[X] →ₐ[R] A) := by
   simp only [IsAlgebraic, injective_iff_map_eq_zero, not_forall, and_comm, exists_prop]
 #align is_algebraic_iff_not_injective isAlgebraic_iff_not_injective
+-/
 
 end
 
@@ -119,30 +125,42 @@ theorem IsIntegral.isAlgebraic [Nontrivial R] {x : A} : IsIntegral R x → IsAlg
 
 variable {R}
 
+#print isAlgebraic_zero /-
 theorem isAlgebraic_zero [Nontrivial R] : IsAlgebraic R (0 : A) :=
   ⟨_, X_ne_zero, aeval_X 0⟩
 #align is_algebraic_zero isAlgebraic_zero
+-/
 
+#print isAlgebraic_algebraMap /-
 /-- An element of `R` is algebraic, when viewed as an element of the `R`-algebra `A`. -/
 theorem isAlgebraic_algebraMap [Nontrivial R] (x : R) : IsAlgebraic R (algebraMap R A x) :=
   ⟨_, X_sub_C_ne_zero x, by rw [_root_.map_sub, aeval_X, aeval_C, sub_self]⟩
 #align is_algebraic_algebra_map isAlgebraic_algebraMap
+-/
 
+#print isAlgebraic_one /-
 theorem isAlgebraic_one [Nontrivial R] : IsAlgebraic R (1 : A) := by rw [← _root_.map_one _];
   exact isAlgebraic_algebraMap 1
 #align is_algebraic_one isAlgebraic_one
+-/
 
+#print isAlgebraic_nat /-
 theorem isAlgebraic_nat [Nontrivial R] (n : ℕ) : IsAlgebraic R (n : A) := by rw [← map_natCast _];
   exact isAlgebraic_algebraMap n
 #align is_algebraic_nat isAlgebraic_nat
+-/
 
+#print isAlgebraic_int /-
 theorem isAlgebraic_int [Nontrivial R] (n : ℤ) : IsAlgebraic R (n : A) := by
   rw [← _root_.map_int_cast (algebraMap R A)]; exact isAlgebraic_algebraMap n
 #align is_algebraic_int isAlgebraic_int
+-/
 
+#print isAlgebraic_rat /-
 theorem isAlgebraic_rat (R : Type u) {A : Type v} [DivisionRing A] [Field R] [Algebra R A] (n : ℚ) :
     IsAlgebraic R (n : A) := by rw [← map_ratCast (algebraMap R A)]; exact isAlgebraic_algebraMap n
 #align is_algebraic_rat isAlgebraic_rat
+-/
 
 #print isAlgebraic_of_mem_rootSet /-
 theorem isAlgebraic_of_mem_rootSet {R : Type u} {A : Type v} [Field R] [Field A] [Algebra R A]
@@ -153,11 +171,14 @@ theorem isAlgebraic_of_mem_rootSet {R : Type u} {A : Type v} [Field R] [Field A]
 
 open IsScalarTower
 
+#print isAlgebraic_algebraMap_of_isAlgebraic /-
 theorem isAlgebraic_algebraMap_of_isAlgebraic {a : S} :
     IsAlgebraic R a → IsAlgebraic R (algebraMap S A a) := fun ⟨f, hf₁, hf₂⟩ =>
   ⟨f, hf₁, by rw [aeval_algebra_map_apply, hf₂, map_zero]⟩
 #align is_algebraic_algebra_map_of_is_algebraic isAlgebraic_algebraMap_of_isAlgebraic
+-/
 
+#print isAlgebraic_algHom_of_isAlgebraic /-
 /-- This is slightly more general than `is_algebraic_algebra_map_of_is_algebraic` in that it
   allows noncommutative intermediate rings `A`. -/
 theorem isAlgebraic_algHom_of_isAlgebraic {B} [Ring B] [Algebra R B] (f : A →ₐ[R] B) {a : A}
@@ -165,24 +186,32 @@ theorem isAlgebraic_algHom_of_isAlgebraic {B} [Ring B] [Algebra R B] (f : A →
   let ⟨p, hp, ha⟩ := h
   ⟨p, hp, by rw [aeval_alg_hom, f.comp_apply, ha, map_zero]⟩
 #align is_algebraic_alg_hom_of_is_algebraic isAlgebraic_algHom_of_isAlgebraic
+-/
 
+#print AlgEquiv.isAlgebraic /-
 /-- Transfer `algebra.is_algebraic` across an `alg_equiv`. -/
 theorem AlgEquiv.isAlgebraic {B} [Ring B] [Algebra R B] (e : A ≃ₐ[R] B)
     (h : Algebra.IsAlgebraic R A) : Algebra.IsAlgebraic R B := fun b => by
   convert ← isAlgebraic_algHom_of_isAlgebraic e.to_alg_hom (h _) <;> apply e.apply_symm_apply
 #align alg_equiv.is_algebraic AlgEquiv.isAlgebraic
+-/
 
+#print AlgEquiv.isAlgebraic_iff /-
 theorem AlgEquiv.isAlgebraic_iff {B} [Ring B] [Algebra R B] (e : A ≃ₐ[R] B) :
     Algebra.IsAlgebraic R A ↔ Algebra.IsAlgebraic R B :=
   ⟨e.IsAlgebraic, e.symm.IsAlgebraic⟩
 #align alg_equiv.is_algebraic_iff AlgEquiv.isAlgebraic_iff
+-/
 
+#print isAlgebraic_algebraMap_iff /-
 theorem isAlgebraic_algebraMap_iff {a : S} (h : Function.Injective (algebraMap S A)) :
     IsAlgebraic R (algebraMap S A a) ↔ IsAlgebraic R a :=
   ⟨fun ⟨p, hp0, hp⟩ => ⟨p, hp0, h (by rwa [map_zero, ← aeval_algebra_map_apply])⟩,
     isAlgebraic_algebraMap_of_isAlgebraic⟩
 #align is_algebraic_algebra_map_iff isAlgebraic_algebraMap_iff
+-/
 
+#print isAlgebraic_of_pow /-
 theorem isAlgebraic_of_pow {r : A} {n : ℕ} (hn : 0 < n) (ht : IsAlgebraic R (r ^ n)) :
     IsAlgebraic R r := by
   obtain ⟨p, p_nonzero, hp⟩ := ht
@@ -190,10 +219,13 @@ theorem isAlgebraic_of_pow {r : A} {n : ℕ} (hn : 0 < n) (ht : IsAlgebraic R (r
   · rwa [Polynomial.expand_ne_zero hn]
   · rwa [Polynomial.expand_aeval n p r]
 #align is_algebraic_of_pow isAlgebraic_of_pow
+-/
 
+#print Transcendental.pow /-
 theorem Transcendental.pow {r : A} (ht : Transcendental R r) {n : ℕ} (hn : 0 < n) :
     Transcendental R (r ^ n) := fun ht' => ht <| isAlgebraic_of_pow hn ht'
 #align transcendental.pow Transcendental.pow
+-/
 
 end zero_ne_one
 
@@ -231,6 +263,7 @@ variable [Algebra K L] [Algebra L A] [Algebra K A] [IsScalarTower K L A]
 
 variable [Algebra R S] [Algebra S A] [Algebra R A] [IsScalarTower R S A]
 
+#print Algebra.isAlgebraic_trans /-
 /-- If L is an algebraic field extension of K and A is an algebraic algebra over L,
 then A is algebraic over K. -/
 theorem isAlgebraic_trans (L_alg : IsAlgebraic K L) (A_alg : IsAlgebraic L A) : IsAlgebraic K A :=
@@ -238,9 +271,11 @@ theorem isAlgebraic_trans (L_alg : IsAlgebraic K L) (A_alg : IsAlgebraic L A) :
   simp only [IsAlgebraic, isAlgebraic_iff_isIntegral] at L_alg A_alg ⊢
   exact isIntegral_trans L_alg A_alg
 #align algebra.is_algebraic_trans Algebra.isAlgebraic_trans
+-/
 
 variable (K L)
 
+#print isAlgebraic_of_larger_base_of_injective /-
 /-- If x is algebraic over R, then x is algebraic over S when S is an extension of R,
   and the map from `R` to `S` is injective. -/
 theorem isAlgebraic_of_larger_base_of_injective (hinj : Function.Injective (algebraMap R S)) {x : A}
@@ -249,38 +284,50 @@ theorem isAlgebraic_of_larger_base_of_injective (hinj : Function.Injective (alge
   ⟨p.map (algebraMap _ _), by
     rwa [Ne.def, ← degree_eq_bot, degree_map_eq_of_injective hinj, degree_eq_bot], by simpa⟩
 #align is_algebraic_of_larger_base_of_injective isAlgebraic_of_larger_base_of_injective
+-/
 
+#print Algebra.isAlgebraic_of_larger_base_of_injective /-
 /-- If A is an algebraic algebra over R, then A is algebraic over S when S is an extension of R,
   and the map from `R` to `S` is injective. -/
 theorem isAlgebraic_of_larger_base_of_injective (hinj : Function.Injective (algebraMap R S))
     (A_alg : IsAlgebraic R A) : IsAlgebraic S A := fun x =>
   isAlgebraic_of_larger_base_of_injective hinj (A_alg x)
 #align algebra.is_algebraic_of_larger_base_of_injective Algebra.isAlgebraic_of_larger_base_of_injective
+-/
 
+#print isAlgebraic_of_larger_base /-
 /-- If x is a algebraic over K, then x is algebraic over L when L is an extension of K -/
 theorem isAlgebraic_of_larger_base {x : A} (A_alg : IsAlgebraic K x) : IsAlgebraic L x :=
   isAlgebraic_of_larger_base_of_injective (algebraMap K L).Injective A_alg
 #align is_algebraic_of_larger_base isAlgebraic_of_larger_base
+-/
 
+#print Algebra.isAlgebraic_of_larger_base /-
 /-- If A is an algebraic algebra over K, then A is algebraic over L when L is an extension of K -/
 theorem isAlgebraic_of_larger_base (A_alg : IsAlgebraic K A) : IsAlgebraic L A :=
   isAlgebraic_of_larger_base_of_injective (algebraMap K L).Injective A_alg
 #align algebra.is_algebraic_of_larger_base Algebra.isAlgebraic_of_larger_base
+-/
 
 variable (K L)
 
+#print Algebra.isIntegral_of_finite /-
 /-- A field extension is integral if it is finite. -/
 theorem isIntegral_of_finite [FiniteDimensional K L] : Algebra.IsIntegral K L := fun x =>
   isIntegral_of_submodule_noetherian ⊤ (IsNoetherian.iff_fg.2 inferInstance) x Algebra.mem_top
 #align algebra.is_integral_of_finite Algebra.isIntegral_of_finite
+-/
 
+#print Algebra.isAlgebraic_of_finite /-
 /-- A field extension is algebraic if it is finite. -/
 theorem isAlgebraic_of_finite [finite : FiniteDimensional K L] : IsAlgebraic K L :=
   Algebra.isAlgebraic_iff_isIntegral.mpr (isIntegral_of_finite K L)
 #align algebra.is_algebraic_of_finite Algebra.isAlgebraic_of_finite
+-/
 
 variable {K L}
 
+#print Algebra.IsAlgebraic.algHom_bijective /-
 theorem IsAlgebraic.algHom_bijective (ha : Algebra.IsAlgebraic K L) (f : L →ₐ[K] L) :
     Function.Bijective f :=
   by
@@ -293,13 +340,17 @@ theorem IsAlgebraic.algHom_bijective (ha : Algebra.IsAlgebraic K L) (f : L →
   obtain ⟨a, ha⟩ := this ⟨b, mem_root_set.2 ⟨hp, he⟩⟩
   exact ⟨a, Subtype.ext_iff.1 ha⟩
 #align algebra.is_algebraic.alg_hom_bijective Algebra.IsAlgebraic.algHom_bijective
+-/
 
+#print AlgHom.bijective /-
 theorem AlgHom.bijective [FiniteDimensional K L] (ϕ : L →ₐ[K] L) : Function.Bijective ϕ :=
   (Algebra.isAlgebraic_of_finite K L).algHom_bijective ϕ
 #align alg_hom.bijective AlgHom.bijective
+-/
 
 variable (K L)
 
+#print Algebra.IsAlgebraic.algEquivEquivAlgHom /-
 /-- Bijection between algebra equivalences and algebra homomorphisms -/
 @[simps]
 noncomputable def IsAlgebraic.algEquivEquivAlgHom (ha : Algebra.IsAlgebraic K L) :
@@ -310,18 +361,22 @@ noncomputable def IsAlgebraic.algEquivEquivAlgHom (ha : Algebra.IsAlgebraic K L)
   right_inv _ := by ext; rfl
   map_mul' _ _ := rfl
 #align algebra.is_algebraic.alg_equiv_equiv_alg_hom Algebra.IsAlgebraic.algEquivEquivAlgHom
+-/
 
+#print algEquivEquivAlgHom /-
 /-- Bijection between algebra equivalences and algebra homomorphisms -/
 @[reducible]
 noncomputable def algEquivEquivAlgHom [FiniteDimensional K L] : (L ≃ₐ[K] L) ≃* (L →ₐ[K] L) :=
   (Algebra.isAlgebraic_of_finite K L).algEquivEquivAlgHom K L
 #align alg_equiv_equiv_alg_hom algEquivEquivAlgHom
+-/
 
 end Algebra
 
 variable {R S : Type _} [CommRing R] [IsDomain R] [CommRing S]
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (y «expr ≠ » (0 : R)) -/
+#print exists_integral_multiple /-
 theorem exists_integral_multiple [Algebra R S] {z : S} (hz : IsAlgebraic R z)
     (inj : ∀ x, algebraMap R S x = 0 → x = 0) :
     ∃ (x : integralClosure R S) (y : _) (_ : y ≠ (0 : R)), z * algebraMap R S y = x :=
@@ -335,8 +390,10 @@ theorem exists_integral_multiple [Algebra R S] {z : S} (hz : IsAlgebraic R z)
       integral_normalization_aeval_eq_zero px inj⟩
   exact ⟨⟨_, x_integral⟩, a, a_ne_zero, rfl⟩
 #align exists_integral_multiple exists_integral_multiple
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (d «expr ≠ » (0 : R)) -/
+#print IsIntegralClosure.exists_smul_eq_mul /-
 /-- A fraction `(a : S) / (b : S)` can be reduced to `(c : S) / (d : R)`,
 if `S` is the integral closure of `R` in an algebraic extension `L` of `R`. -/
 theorem IsIntegralClosure.exists_smul_eq_mul {L : Type _} [Field L] [Algebra R S] [Algebra S L]
@@ -354,11 +411,13 @@ theorem IsIntegralClosure.exists_smul_eq_mul {L : Type _} [Field L] [Algebra R S
   rw [← mul_assoc _ (_ / _), mul_div_cancel' (algebraMap S L a), mul_comm]
   exact mt ((injective_iff_map_eq_zero _).mp (IsIntegralClosure.algebraMap_injective S R L) _) hb
 #align is_integral_closure.exists_smul_eq_mul IsIntegralClosure.exists_smul_eq_mul
+-/
 
 section Field
 
 variable {K L : Type _} [Field K] [Field L] [Algebra K L] (A : Subalgebra K L)
 
+#print inv_eq_of_aeval_divX_ne_zero /-
 theorem inv_eq_of_aeval_divX_ne_zero {x : L} {p : K[X]} (aeval_ne : aeval x (divX p) ≠ 0) :
     x⁻¹ = aeval x (divX p) / (aeval x p - algebraMap _ _ (p.coeff 0)) :=
   by
@@ -367,7 +426,9 @@ theorem inv_eq_of_aeval_divX_ne_zero {x : L} {p : K[X]} (aeval_ne : aeval x (div
   rw [AlgHom.map_add, AlgHom.map_mul, aeval_X, aeval_C]
   exact aeval_ne
 #align inv_eq_of_aeval_div_X_ne_zero inv_eq_of_aeval_divX_ne_zero
+-/
 
+#print inv_eq_of_root_of_coeff_zero_ne_zero /-
 theorem inv_eq_of_root_of_coeff_zero_ne_zero {x : L} {p : K[X]} (aeval_eq : aeval x p = 0)
     (coeff_zero_ne : p.coeff 0 ≠ 0) : x⁻¹ = -(aeval x (divX p) / algebraMap _ _ (p.coeff 0)) :=
   by
@@ -378,7 +439,9 @@ theorem inv_eq_of_root_of_coeff_zero_ne_zero {x : L} {p : K[X]} (aeval_eq : aeva
   conv_rhs => rw [← div_X_mul_X_add p]
   rw [AlgHom.map_add, AlgHom.map_mul, h, MulZeroClass.zero_mul, zero_add, aeval_C]
 #align inv_eq_of_root_of_coeff_zero_ne_zero inv_eq_of_root_of_coeff_zero_ne_zero
+-/
 
+#print Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero /-
 theorem Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero {x : A} {p : K[X]}
     (aeval_eq : aeval x p = 0) (coeff_zero_ne : p.coeff 0 ≠ 0) : (x⁻¹ : L) ∈ A :=
   by
@@ -388,7 +451,9 @@ theorem Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero {x : A} {p : K[X]}
   rw [inv_eq_of_root_of_coeff_zero_ne_zero this coeff_zero_ne, div_eq_inv_mul, Algebra.smul_def,
     map_inv₀, map_neg, inv_neg, neg_mul, Subalgebra.aeval_coe]
 #align subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero
+-/
 
+#print Subalgebra.inv_mem_of_algebraic /-
 theorem Subalgebra.inv_mem_of_algebraic {x : A} (hx : IsAlgebraic K (x : L)) : (x⁻¹ : L) ∈ A :=
   by
   obtain ⟨p, ne_zero, aeval_eq⟩ := hx
@@ -407,7 +472,9 @@ theorem Subalgebra.inv_mem_of_algebraic {x : A} (hx : IsAlgebraic K (x : L)) : (
     · rw [x_eq, Subalgebra.coe_zero, inv_zero]
       exact A.zero_mem
 #align subalgebra.inv_mem_of_algebraic Subalgebra.inv_mem_of_algebraic
+-/
 
+#print Subalgebra.isField_of_algebraic /-
 /-- In an algebraic extension L/K, an intermediate subalgebra is a field. -/
 theorem Subalgebra.isField_of_algebraic (hKL : Algebra.IsAlgebraic K L) : IsField A :=
   { show Nontrivial A by infer_instance, Subalgebra.toCommRing A with
@@ -415,6 +482,7 @@ theorem Subalgebra.isField_of_algebraic (hKL : Algebra.IsAlgebraic K L) : IsFiel
       ⟨⟨a⁻¹, A.inv_mem_of_algebraic (hKL a)⟩,
         Subtype.ext (mul_inv_cancel (mt (Subalgebra.coe_eq_zero _).mp ha))⟩ }
 #align subalgebra.is_field_of_algebraic Subalgebra.isField_of_algebraic
+-/
 
 end Field
 
@@ -453,11 +521,13 @@ theorem polynomial_smul_apply [Semiring R'] [SMul R' S'] (p : R'[X]) (f : R' →
 #align polynomial_smul_apply polynomial_smul_apply
 -/
 
+#print polynomial_smul_apply' /-
 @[simp]
 theorem polynomial_smul_apply' [CommSemiring R'] [Semiring S'] [Algebra R' S'] [SMul S' T']
     (p : R'[X]) (f : S' → T') (x : S') : (p • f) x = aeval x p • f x :=
   rfl
 #align polynomial_smul_apply' polynomial_smul_apply'
+-/
 
 variable [CommSemiring R'] [CommSemiring S'] [CommSemiring T'] [Algebra R' S'] [Algebra S' T']
 
@@ -483,17 +553,21 @@ noncomputable def Polynomial.algebraPi : Algebra R'[X] (S' → T') :=
 
 attribute [local instance] Polynomial.algebraPi
 
+#print Polynomial.algebraMap_pi_eq_aeval /-
 @[simp]
 theorem Polynomial.algebraMap_pi_eq_aeval :
     (algebraMap R'[X] (S' → T') : R'[X] → S' → T') = fun p z => algebraMap _ _ (aeval z p) :=
   rfl
 #align polynomial.algebra_map_pi_eq_aeval Polynomial.algebraMap_pi_eq_aeval
+-/
 
+#print Polynomial.algebraMap_pi_self_eq_eval /-
 @[simp]
 theorem Polynomial.algebraMap_pi_self_eq_eval :
     (algebraMap R'[X] (R' → R') : R'[X] → R' → R') = fun p z => eval z p :=
   rfl
 #align polynomial.algebra_map_pi_self_eq_eval Polynomial.algebraMap_pi_self_eq_eval
+-/
 
 end Pi
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

@@ -321,7 +321,7 @@ end Algebra
 
 variable {R S : Type _} [CommRing R] [IsDomain R] [CommRing S]
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y «expr ≠ » (0 : R)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (y «expr ≠ » (0 : R)) -/
 theorem exists_integral_multiple [Algebra R S] {z : S} (hz : IsAlgebraic R z)
     (inj : ∀ x, algebraMap R S x = 0 → x = 0) :
     ∃ (x : integralClosure R S) (y : _) (_ : y ≠ (0 : R)), z * algebraMap R S y = x :=
@@ -336,7 +336,7 @@ theorem exists_integral_multiple [Algebra R S] {z : S} (hz : IsAlgebraic R z)
   exact ⟨⟨_, x_integral⟩, a, a_ne_zero, rfl⟩
 #align exists_integral_multiple exists_integral_multiple
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (d «expr ≠ » (0 : R)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (d «expr ≠ » (0 : R)) -/
 /-- A fraction `(a : S) / (b : S)` can be reduced to `(c : S) / (d : R)`,
 if `S` is the integral closure of `R` in an algebraic extension `L` of `R`. -/
 theorem IsIntegralClosure.exists_smul_eq_mul {L : Type _} [Field L] [Algebra R S] [Algebra S L]

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

@@ -169,7 +169,7 @@ theorem isAlgebraic_algHom_of_isAlgebraic {B} [Ring B] [Algebra R B] (f : A →
 /-- Transfer `algebra.is_algebraic` across an `alg_equiv`. -/
 theorem AlgEquiv.isAlgebraic {B} [Ring B] [Algebra R B] (e : A ≃ₐ[R] B)
     (h : Algebra.IsAlgebraic R A) : Algebra.IsAlgebraic R B := fun b => by
-  convert← isAlgebraic_algHom_of_isAlgebraic e.to_alg_hom (h _) <;> apply e.apply_symm_apply
+  convert ← isAlgebraic_algHom_of_isAlgebraic e.to_alg_hom (h _) <;> apply e.apply_symm_apply
 #align alg_equiv.is_algebraic AlgEquiv.isAlgebraic
 
 theorem AlgEquiv.isAlgebraic_iff {B} [Ring B] [Algebra R B] (e : A ≃ₐ[R] B) :

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

@@ -235,7 +235,7 @@ variable [Algebra R S] [Algebra S A] [Algebra R A] [IsScalarTower R S A]
 then A is algebraic over K. -/
 theorem isAlgebraic_trans (L_alg : IsAlgebraic K L) (A_alg : IsAlgebraic L A) : IsAlgebraic K A :=
   by
-  simp only [IsAlgebraic, isAlgebraic_iff_isIntegral] at L_alg A_alg⊢
+  simp only [IsAlgebraic, isAlgebraic_iff_isIntegral] at L_alg A_alg ⊢
   exact isIntegral_trans L_alg A_alg
 #align algebra.is_algebraic_trans Algebra.isAlgebraic_trans
 
@@ -324,7 +324,7 @@ variable {R S : Type _} [CommRing R] [IsDomain R] [CommRing S]
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y «expr ≠ » (0 : R)) -/
 theorem exists_integral_multiple [Algebra R S] {z : S} (hz : IsAlgebraic R z)
     (inj : ∀ x, algebraMap R S x = 0 → x = 0) :
-    ∃ (x : integralClosure R S)(y : _)(_ : y ≠ (0 : R)), z * algebraMap R S y = x :=
+    ∃ (x : integralClosure R S) (y : _) (_ : y ≠ (0 : R)), z * algebraMap R S y = x :=
   by
   rcases hz with ⟨p, p_ne_zero, px⟩
   set a := p.leading_coeff with a_def
@@ -342,7 +342,7 @@ if `S` is the integral closure of `R` in an algebraic extension `L` of `R`. -/
 theorem IsIntegralClosure.exists_smul_eq_mul {L : Type _} [Field L] [Algebra R S] [Algebra S L]
     [Algebra R L] [IsScalarTower R S L] [IsIntegralClosure S R L] (h : Algebra.IsAlgebraic R L)
     (inj : Function.Injective (algebraMap R L)) (a : S) {b : S} (hb : b ≠ 0) :
-    ∃ (c : S)(d : _)(_ : d ≠ (0 : R)), d • a = b * c :=
+    ∃ (c : S) (d : _) (_ : d ≠ (0 : R)), d • a = b * c :=
   by
   obtain ⟨c, d, d_ne, hx⟩ :=
     exists_integral_multiple (h (algebraMap _ L a / algebraMap _ L b))
@@ -392,7 +392,7 @@ theorem Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero {x : A} {p : K[X]}
 theorem Subalgebra.inv_mem_of_algebraic {x : A} (hx : IsAlgebraic K (x : L)) : (x⁻¹ : L) ∈ A :=
   by
   obtain ⟨p, ne_zero, aeval_eq⟩ := hx
-  rw [Subalgebra.aeval_coe, Subalgebra.coe_eq_zero] at aeval_eq
+  rw [Subalgebra.aeval_coe, Subalgebra.coe_eq_zero] at aeval_eq 
   revert ne_zero aeval_eq
   refine' p.rec_on_horner _ _ _
   · intro h
@@ -401,7 +401,7 @@ theorem Subalgebra.inv_mem_of_algebraic {x : A} (hx : IsAlgebraic K (x : L)) : (
     refine' A.inv_mem_of_root_of_coeff_zero_ne_zero aeval_eq _
     rwa [coeff_add, hp, zero_add, coeff_C, if_pos rfl]
   · intro p hp ih ne_zero aeval_eq
-    rw [AlgHom.map_mul, aeval_X, mul_eq_zero] at aeval_eq
+    rw [AlgHom.map_mul, aeval_X, mul_eq_zero] at aeval_eq 
     cases' aeval_eq with aeval_eq x_eq
     · exact ih hp aeval_eq
     · rw [x_eq, Subalgebra.coe_zero, inv_zero]

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

@@ -95,12 +95,10 @@ theorem Algebra.isAlgebraic_iff : Algebra.IsAlgebraic R A ↔ (⊤ : Subalgebra
   simp only [Algebra.mem_top, forall_prop_of_true, iff_self_iff]
 #align algebra.is_algebraic_iff Algebra.isAlgebraic_iff
 
-#print isAlgebraic_iff_not_injective /-
 theorem isAlgebraic_iff_not_injective {x : A} :
     IsAlgebraic R x ↔ ¬Function.Injective (Polynomial.aeval x : R[X] →ₐ[R] A) := by
   simp only [IsAlgebraic, injective_iff_map_eq_zero, not_forall, and_comm, exists_prop]
 #align is_algebraic_iff_not_injective isAlgebraic_iff_not_injective
--/
 
 end
 
@@ -455,13 +453,11 @@ theorem polynomial_smul_apply [Semiring R'] [SMul R' S'] (p : R'[X]) (f : R' →
 #align polynomial_smul_apply polynomial_smul_apply
 -/
 
-#print polynomial_smul_apply' /-
 @[simp]
 theorem polynomial_smul_apply' [CommSemiring R'] [Semiring S'] [Algebra R' S'] [SMul S' T']
     (p : R'[X]) (f : S' → T') (x : S') : (p • f) x = aeval x p • f x :=
   rfl
 #align polynomial_smul_apply' polynomial_smul_apply'
--/
 
 variable [CommSemiring R'] [CommSemiring S'] [CommSemiring T'] [Algebra R' S'] [Algebra S' T']
 

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

@@ -27,7 +27,7 @@ a tower of algebraic field extensions is algebraic.
 
 universe u v w
 
-open Classical Polynomial
+open scoped Classical Polynomial
 
 open Polynomial
 

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

@@ -76,12 +76,6 @@ def Algebra.IsAlgebraic : Prop :=
 
 variable {R A}
 
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 /-- A subalgebra is algebraic if and only if it is algebraic as an algebra. -/
 theorem Subalgebra.isAlgebraic_iff (S : Subalgebra R A) :
     S.IsAlgebraic ↔ @Algebra.IsAlgebraic R S _ _ S.Algebra :=
@@ -94,12 +88,6 @@ theorem Subalgebra.isAlgebraic_iff (S : Subalgebra R A) :
   rw [← aeval_alg_hom_apply, S.val_apply]
 #align subalgebra.is_algebraic_iff Subalgebra.isAlgebraic_iff
 
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 /-- An algebra is algebraic if and only if it is algebraic as a subalgebra. -/
 theorem Algebra.isAlgebraic_iff : Algebra.IsAlgebraic R A ↔ (⊤ : Subalgebra R A).IsAlgebraic :=
   by
@@ -133,63 +121,27 @@ theorem IsIntegral.isAlgebraic [Nontrivial R] {x : A} : IsIntegral R x → IsAlg
 
 variable {R}
 
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 theorem isAlgebraic_zero [Nontrivial R] : IsAlgebraic R (0 : A) :=
   ⟨_, X_ne_zero, aeval_X 0⟩
 #align is_algebraic_zero isAlgebraic_zero
 
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 /-- An element of `R` is algebraic, when viewed as an element of the `R`-algebra `A`. -/
 theorem isAlgebraic_algebraMap [Nontrivial R] (x : R) : IsAlgebraic R (algebraMap R A x) :=
   ⟨_, X_sub_C_ne_zero x, by rw [_root_.map_sub, aeval_X, aeval_C, sub_self]⟩
 #align is_algebraic_algebra_map isAlgebraic_algebraMap
 
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 theorem isAlgebraic_one [Nontrivial R] : IsAlgebraic R (1 : A) := by rw [← _root_.map_one _];
   exact isAlgebraic_algebraMap 1
 #align is_algebraic_one isAlgebraic_one
 
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 theorem isAlgebraic_nat [Nontrivial R] (n : ℕ) : IsAlgebraic R (n : A) := by rw [← map_natCast _];
   exact isAlgebraic_algebraMap n
 #align is_algebraic_nat isAlgebraic_nat
 
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 theorem isAlgebraic_int [Nontrivial R] (n : ℤ) : IsAlgebraic R (n : A) := by
   rw [← _root_.map_int_cast (algebraMap R A)]; exact isAlgebraic_algebraMap n
 #align is_algebraic_int isAlgebraic_int
 
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 theorem isAlgebraic_rat (R : Type u) {A : Type v} [DivisionRing A] [Field R] [Algebra R A] (n : ℚ) :
     IsAlgebraic R (n : A) := by rw [← map_ratCast (algebraMap R A)]; exact isAlgebraic_algebraMap n
 #align is_algebraic_rat isAlgebraic_rat
@@ -203,17 +155,11 @@ theorem isAlgebraic_of_mem_rootSet {R : Type u} {A : Type v} [Field R] [Field A]
 
 open IsScalarTower
 
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 theorem isAlgebraic_algebraMap_of_isAlgebraic {a : S} :
     IsAlgebraic R a → IsAlgebraic R (algebraMap S A a) := fun ⟨f, hf₁, hf₂⟩ =>
   ⟨f, hf₁, by rw [aeval_algebra_map_apply, hf₂, map_zero]⟩
 #align is_algebraic_algebra_map_of_is_algebraic isAlgebraic_algebraMap_of_isAlgebraic
 
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 /-- This is slightly more general than `is_algebraic_algebra_map_of_is_algebraic` in that it
   allows noncommutative intermediate rings `A`. -/
 theorem isAlgebraic_algHom_of_isAlgebraic {B} [Ring B] [Algebra R B] (f : A →ₐ[R] B) {a : A}
@@ -222,44 +168,23 @@ theorem isAlgebraic_algHom_of_isAlgebraic {B} [Ring B] [Algebra R B] (f : A →
   ⟨p, hp, by rw [aeval_alg_hom, f.comp_apply, ha, map_zero]⟩
 #align is_algebraic_alg_hom_of_is_algebraic isAlgebraic_algHom_of_isAlgebraic
 
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-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3)] {B : Type.{u3}} [_inst_8 : Ring.{u3} B] [_inst_9 : Algebra.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B _inst_8)], (AlgEquiv.{u1, u2, u3} R A B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3) (Ring.toSemiring.{u3} B _inst_8) _inst_4 _inst_9) -> (Algebra.IsAlgebraic.{u1, u2} R A _inst_1 _inst_3 _inst_4) -> (Algebra.IsAlgebraic.{u1, u3} R B _inst_1 _inst_8 _inst_9)
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-Case conversion may be inaccurate. Consider using '#align alg_equiv.is_algebraic AlgEquiv.isAlgebraicₓ'. -/
 /-- Transfer `algebra.is_algebraic` across an `alg_equiv`. -/
 theorem AlgEquiv.isAlgebraic {B} [Ring B] [Algebra R B] (e : A ≃ₐ[R] B)
     (h : Algebra.IsAlgebraic R A) : Algebra.IsAlgebraic R B := fun b => by
   convert← isAlgebraic_algHom_of_isAlgebraic e.to_alg_hom (h _) <;> apply e.apply_symm_apply
 #align alg_equiv.is_algebraic AlgEquiv.isAlgebraic
 
-/- warning: alg_equiv.is_algebraic_iff -> AlgEquiv.isAlgebraic_iff is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3)] {B : Type.{u3}} [_inst_8 : Ring.{u3} B] [_inst_9 : Algebra.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B _inst_8)], (AlgEquiv.{u1, u2, u3} R A B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3) (Ring.toSemiring.{u3} B _inst_8) _inst_4 _inst_9) -> (Iff (Algebra.IsAlgebraic.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Algebra.IsAlgebraic.{u1, u3} R B _inst_1 _inst_8 _inst_9))
-but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_3 : Ring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3)] {B : Type.{u1}} [_inst_8 : Ring.{u1} B] [_inst_9 : Algebra.{u2, u1} R B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} B _inst_8)], (AlgEquiv.{u2, u3, u1} R A B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3) (Ring.toSemiring.{u1} B _inst_8) _inst_4 _inst_9) -> (Iff (Algebra.IsAlgebraic.{u2, u3} R A _inst_1 _inst_3 _inst_4) (Algebra.IsAlgebraic.{u2, u1} R B _inst_1 _inst_8 _inst_9))
-Case conversion may be inaccurate. Consider using '#align alg_equiv.is_algebraic_iff AlgEquiv.isAlgebraic_iffₓ'. -/
 theorem AlgEquiv.isAlgebraic_iff {B} [Ring B] [Algebra R B] (e : A ≃ₐ[R] B) :
     Algebra.IsAlgebraic R A ↔ Algebra.IsAlgebraic R B :=
   ⟨e.IsAlgebraic, e.symm.IsAlgebraic⟩
 #align alg_equiv.is_algebraic_iff AlgEquiv.isAlgebraic_iff
 
-/- warning: is_algebraic_algebra_map_iff -> isAlgebraic_algebraMap_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_algebraic_algebra_map_iff isAlgebraic_algebraMap_iffₓ'. -/
 theorem isAlgebraic_algebraMap_iff {a : S} (h : Function.Injective (algebraMap S A)) :
     IsAlgebraic R (algebraMap S A a) ↔ IsAlgebraic R a :=
   ⟨fun ⟨p, hp0, hp⟩ => ⟨p, hp0, h (by rwa [map_zero, ← aeval_algebra_map_apply])⟩,
     isAlgebraic_algebraMap_of_isAlgebraic⟩
 #align is_algebraic_algebra_map_iff isAlgebraic_algebraMap_iff
 
-/- warning: is_algebraic_of_pow -> isAlgebraic_of_pow is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3)] {r : A} {n : Nat}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n) -> (IsAlgebraic.{u1, u2} R A _inst_1 _inst_3 _inst_4 (HPow.hPow.{u2, 0, u2} A Nat A (instHPow.{u2, 0} A Nat (Monoid.Pow.{u2} A (Ring.toMonoid.{u2} A _inst_3))) r n)) -> (IsAlgebraic.{u1, u2} R A _inst_1 _inst_3 _inst_4 r)
-but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3)] {r : A} {n : Nat}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) -> (IsAlgebraic.{u1, u2} R A _inst_1 _inst_3 _inst_4 (HPow.hPow.{u2, 0, u2} A Nat A (instHPow.{u2, 0} A Nat (Monoid.Pow.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A _inst_3))))) r n)) -> (IsAlgebraic.{u1, u2} R A _inst_1 _inst_3 _inst_4 r)
-Case conversion may be inaccurate. Consider using '#align is_algebraic_of_pow isAlgebraic_of_powₓ'. -/
 theorem isAlgebraic_of_pow {r : A} {n : ℕ} (hn : 0 < n) (ht : IsAlgebraic R (r ^ n)) :
     IsAlgebraic R r := by
   obtain ⟨p, p_nonzero, hp⟩ := ht
@@ -268,12 +193,6 @@ theorem isAlgebraic_of_pow {r : A} {n : ℕ} (hn : 0 < n) (ht : IsAlgebraic R (r
   · rwa [Polynomial.expand_aeval n p r]
 #align is_algebraic_of_pow isAlgebraic_of_pow
 
-/- warning: transcendental.pow -> Transcendental.pow is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3)] {r : A}, (Transcendental.{u1, u2} R A _inst_1 _inst_3 _inst_4 r) -> (forall {n : Nat}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n) -> (Transcendental.{u1, u2} R A _inst_1 _inst_3 _inst_4 (HPow.hPow.{u2, 0, u2} A Nat A (instHPow.{u2, 0} A Nat (Monoid.Pow.{u2} A (Ring.toMonoid.{u2} A _inst_3))) r n)))
-but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3)] {r : A}, (Transcendental.{u1, u2} R A _inst_1 _inst_3 _inst_4 r) -> (forall {n : Nat}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) -> (Transcendental.{u1, u2} R A _inst_1 _inst_3 _inst_4 (HPow.hPow.{u2, 0, u2} A Nat A (instHPow.{u2, 0} A Nat (Monoid.Pow.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A _inst_3))))) r n)))
-Case conversion may be inaccurate. Consider using '#align transcendental.pow Transcendental.powₓ'. -/
 theorem Transcendental.pow {r : A} (ht : Transcendental R r) {n : ℕ} (hn : 0 < n) :
     Transcendental R (r ^ n) := fun ht' => ht <| isAlgebraic_of_pow hn ht'
 #align transcendental.pow Transcendental.pow
@@ -314,12 +233,6 @@ variable [Algebra K L] [Algebra L A] [Algebra K A] [IsScalarTower K L A]
 
 variable [Algebra R S] [Algebra S A] [Algebra R A] [IsScalarTower R S A]
 
-/- warning: algebra.is_algebraic_trans -> Algebra.isAlgebraic_trans is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} {L : Type.{u2}} {A : Type.{u3}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_5 : CommRing.{u3} A] [_inst_6 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_7 : Algebra.{u2, u3} L A (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))] [_inst_8 : Algebra.{u1, u3} K A (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))] [_inst_9 : IsScalarTower.{u1, u2, u3} K L A (SMulZeroClass.toHasSmul.{u1, u2} K L (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} K L (MulZeroClass.toHasZero.{u1} K (MulZeroOneClass.toMulZeroClass.{u1} K (MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} K L (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (Module.toMulActionWithZero.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6))))) (SMulZeroClass.toHasSmul.{u2, u3} L A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u2, u3} L A (MulZeroClass.toHasZero.{u2} L (MulZeroOneClass.toMulZeroClass.{u2} L (MonoidWithZero.toMulZeroOneClass.{u2} L (Semiring.toMonoidWithZero.{u2} L (CommSemiring.toSemiring.{u2} L (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u2, u3} L A (Semiring.toMonoidWithZero.{u2} L (CommSemiring.toSemiring.{u2} L (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (Module.toMulActionWithZero.{u2, u3} L A (CommSemiring.toSemiring.{u2} L (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))))) (Algebra.toModule.{u2, u3} L A (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)) _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u3} K A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} K A (MulZeroClass.toHasZero.{u1} K (MulZeroOneClass.toMulZeroClass.{u1} K (MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} K A (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (Module.toMulActionWithZero.{u1, u3} K A (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))))) (Algebra.toModule.{u1, u3} K A (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)) _inst_8)))))], (Algebra.IsAlgebraic.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)) _inst_6) -> (Algebra.IsAlgebraic.{u2, u3} L A (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (CommRing.toRing.{u3} A _inst_5) _inst_7) -> (Algebra.IsAlgebraic.{u1, u3} K A (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (CommRing.toRing.{u3} A _inst_5) _inst_8)
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-  forall {K : Type.{u3}} {L : Type.{u2}} {A : Type.{u1}} [_inst_1 : Field.{u3} K] [_inst_2 : Field.{u2} L] [_inst_5 : CommRing.{u1} A] [_inst_6 : Algebra.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] [_inst_7 : Algebra.{u2, u1} L A (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))] [_inst_8 : Algebra.{u3, u1} K A (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))] [_inst_9 : IsScalarTower.{u3, u2, u1} K L A (Algebra.toSMul.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6) (Algebra.toSMul.{u2, u1} L A (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)) _inst_7) (Algebra.toSMul.{u3, u1} K A (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)) _inst_8)], (Algebra.IsAlgebraic.{u3, u2} K L (EuclideanDomain.toCommRing.{u3} K (Field.toEuclideanDomain.{u3} K _inst_1)) (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)) _inst_6) -> (Algebra.IsAlgebraic.{u2, u1} L A (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (CommRing.toRing.{u1} A _inst_5) _inst_7) -> (Algebra.IsAlgebraic.{u3, u1} K A (EuclideanDomain.toCommRing.{u3} K (Field.toEuclideanDomain.{u3} K _inst_1)) (CommRing.toRing.{u1} A _inst_5) _inst_8)
-Case conversion may be inaccurate. Consider using '#align algebra.is_algebraic_trans Algebra.isAlgebraic_transₓ'. -/
 /-- If L is an algebraic field extension of K and A is an algebraic algebra over L,
 then A is algebraic over K. -/
 theorem isAlgebraic_trans (L_alg : IsAlgebraic K L) (A_alg : IsAlgebraic L A) : IsAlgebraic K A :=
@@ -330,9 +243,6 @@ theorem isAlgebraic_trans (L_alg : IsAlgebraic K L) (A_alg : IsAlgebraic L A) :
 
 variable (K L)
 
-/- warning: is_algebraic_of_larger_base_of_injective -> isAlgebraic_of_larger_base_of_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_algebraic_of_larger_base_of_injective isAlgebraic_of_larger_base_of_injectiveₓ'. -/
 /-- If x is algebraic over R, then x is algebraic over S when S is an extension of R,
   and the map from `R` to `S` is injective. -/
 theorem isAlgebraic_of_larger_base_of_injective (hinj : Function.Injective (algebraMap R S)) {x : A}
@@ -342,9 +252,6 @@ theorem isAlgebraic_of_larger_base_of_injective (hinj : Function.Injective (alge
     rwa [Ne.def, ← degree_eq_bot, degree_map_eq_of_injective hinj, degree_eq_bot], by simpa⟩
 #align is_algebraic_of_larger_base_of_injective isAlgebraic_of_larger_base_of_injective
 
-/- warning: algebra.is_algebraic_of_larger_base_of_injective -> Algebra.isAlgebraic_of_larger_base_of_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.is_algebraic_of_larger_base_of_injective Algebra.isAlgebraic_of_larger_base_of_injectiveₓ'. -/
 /-- If A is an algebraic algebra over R, then A is algebraic over S when S is an extension of R,
   and the map from `R` to `S` is injective. -/
 theorem isAlgebraic_of_larger_base_of_injective (hinj : Function.Injective (algebraMap R S))
@@ -352,23 +259,11 @@ theorem isAlgebraic_of_larger_base_of_injective (hinj : Function.Injective (alge
   isAlgebraic_of_larger_base_of_injective hinj (A_alg x)
 #align algebra.is_algebraic_of_larger_base_of_injective Algebra.isAlgebraic_of_larger_base_of_injective
 
-/- warning: is_algebraic_of_larger_base -> isAlgebraic_of_larger_base is a dubious translation:
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(DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} K L (MulZeroClass.toHasZero.{u1} K (MulZeroOneClass.toMulZeroClass.{u1} K (MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} K L (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (Module.toMulActionWithZero.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6))))) (SMulZeroClass.toHasSmul.{u2, u3} L A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u2, u3} L A (MulZeroClass.toHasZero.{u2} L (MulZeroOneClass.toMulZeroClass.{u2} L (MonoidWithZero.toMulZeroOneClass.{u2} L (Semiring.toMonoidWithZero.{u2} L (CommSemiring.toSemiring.{u2} L (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u2, u3} L A (Semiring.toMonoidWithZero.{u2} L (CommSemiring.toSemiring.{u2} L (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (Module.toMulActionWithZero.{u2, u3} L A (CommSemiring.toSemiring.{u2} L (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))))) (Algebra.toModule.{u2, u3} L A (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)) _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u3} K A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} K A (MulZeroClass.toHasZero.{u1} K (MulZeroOneClass.toMulZeroClass.{u1} K (MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} K A (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (Module.toMulActionWithZero.{u1, u3} K A (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))))) (Algebra.toModule.{u1, u3} K A (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)) _inst_8)))))] {x : A}, (IsAlgebraic.{u1, u3} K A (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (CommRing.toRing.{u3} A _inst_5) _inst_8 x) -> (IsAlgebraic.{u2, u3} L A (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (CommRing.toRing.{u3} A _inst_5) _inst_7 x)
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-  forall (K : Type.{u3}) (L : Type.{u1}) {A : Type.{u2}} [_inst_1 : Field.{u3} K] [_inst_2 : Field.{u1} L] [_inst_5 : CommRing.{u2} A] [_inst_6 : Algebra.{u3, u1} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] [_inst_7 : Algebra.{u1, u2} L A (Semifield.toCommSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5))] [_inst_8 : Algebra.{u3, u2} K A (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5))] [_inst_9 : IsScalarTower.{u3, u1, u2} K L A (Algebra.toSMul.{u3, u1} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6) (Algebra.toSMul.{u1, u2} L A (Semifield.toCommSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)) _inst_7) (Algebra.toSMul.{u3, u2} K A (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)) _inst_8)] {x : A}, (IsAlgebraic.{u3, u2} K A (EuclideanDomain.toCommRing.{u3} K (Field.toEuclideanDomain.{u3} K _inst_1)) (CommRing.toRing.{u2} A _inst_5) _inst_8 x) -> (IsAlgebraic.{u1, u2} L A (EuclideanDomain.toCommRing.{u1} L (Field.toEuclideanDomain.{u1} L _inst_2)) (CommRing.toRing.{u2} A _inst_5) _inst_7 x)
-Case conversion may be inaccurate. Consider using '#align is_algebraic_of_larger_base isAlgebraic_of_larger_baseₓ'. -/
 /-- If x is a algebraic over K, then x is algebraic over L when L is an extension of K -/
 theorem isAlgebraic_of_larger_base {x : A} (A_alg : IsAlgebraic K x) : IsAlgebraic L x :=
   isAlgebraic_of_larger_base_of_injective (algebraMap K L).Injective A_alg
 #align is_algebraic_of_larger_base isAlgebraic_of_larger_base
 
-/- warning: algebra.is_algebraic_of_larger_base -> Algebra.isAlgebraic_of_larger_base is a dubious translation:
-lean 3 declaration is
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(DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} K L (MulZeroClass.toHasZero.{u1} K (MulZeroOneClass.toMulZeroClass.{u1} K (MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} K L (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (Module.toMulActionWithZero.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6))))) (SMulZeroClass.toHasSmul.{u2, u3} L A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u2, u3} L A (MulZeroClass.toHasZero.{u2} L (MulZeroOneClass.toMulZeroClass.{u2} L (MonoidWithZero.toMulZeroOneClass.{u2} L (Semiring.toMonoidWithZero.{u2} L (CommSemiring.toSemiring.{u2} L (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u2, u3} L A (Semiring.toMonoidWithZero.{u2} L (CommSemiring.toSemiring.{u2} L (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (Module.toMulActionWithZero.{u2, u3} L A (CommSemiring.toSemiring.{u2} L (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))))) (Algebra.toModule.{u2, u3} L A (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)) _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u3} K A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} K A (MulZeroClass.toHasZero.{u1} K (MulZeroOneClass.toMulZeroClass.{u1} K (MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} K A (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (Module.toMulActionWithZero.{u1, u3} K A (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))))) (Algebra.toModule.{u1, u3} K A (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)) _inst_8)))))], (Algebra.IsAlgebraic.{u1, u3} K A (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (CommRing.toRing.{u3} A _inst_5) _inst_8) -> (Algebra.IsAlgebraic.{u2, u3} L A (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (CommRing.toRing.{u3} A _inst_5) _inst_7)
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-Case conversion may be inaccurate. Consider using '#align algebra.is_algebraic_of_larger_base Algebra.isAlgebraic_of_larger_baseₓ'. -/
 /-- If A is an algebraic algebra over K, then A is algebraic over L when L is an extension of K -/
 theorem isAlgebraic_of_larger_base (A_alg : IsAlgebraic K A) : IsAlgebraic L A :=
   isAlgebraic_of_larger_base_of_injective (algebraMap K L).Injective A_alg
@@ -376,23 +271,11 @@ theorem isAlgebraic_of_larger_base (A_alg : IsAlgebraic K A) : IsAlgebraic L A :
 
 variable (K L)
 
-/- warning: algebra.is_integral_of_finite -> Algebra.isIntegral_of_finite is a dubious translation:
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-  forall (K : Type.{u1}) (L : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_6 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_14 : FiniteDimensional.{u1, u2} K L (Field.toDivisionRing.{u1} K _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6)], Algebra.IsIntegral.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)) _inst_6
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-Case conversion may be inaccurate. Consider using '#align algebra.is_integral_of_finite Algebra.isIntegral_of_finiteₓ'. -/
 /-- A field extension is integral if it is finite. -/
 theorem isIntegral_of_finite [FiniteDimensional K L] : Algebra.IsIntegral K L := fun x =>
   isIntegral_of_submodule_noetherian ⊤ (IsNoetherian.iff_fg.2 inferInstance) x Algebra.mem_top
 #align algebra.is_integral_of_finite Algebra.isIntegral_of_finite
 
-/- warning: algebra.is_algebraic_of_finite -> Algebra.isAlgebraic_of_finite is a dubious translation:
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-  forall (K : Type.{u1}) (L : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_6 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [finite : FiniteDimensional.{u1, u2} K L (Field.toDivisionRing.{u1} K _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6)], Algebra.IsAlgebraic.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)) _inst_6
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-Case conversion may be inaccurate. Consider using '#align algebra.is_algebraic_of_finite Algebra.isAlgebraic_of_finiteₓ'. -/
 /-- A field extension is algebraic if it is finite. -/
 theorem isAlgebraic_of_finite [finite : FiniteDimensional K L] : IsAlgebraic K L :=
   Algebra.isAlgebraic_iff_isIntegral.mpr (isIntegral_of_finite K L)
@@ -400,9 +283,6 @@ theorem isAlgebraic_of_finite [finite : FiniteDimensional K L] : IsAlgebraic K L
 
 variable {K L}
 
-/- warning: algebra.is_algebraic.alg_hom_bijective -> Algebra.IsAlgebraic.algHom_bijective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.is_algebraic.alg_hom_bijective Algebra.IsAlgebraic.algHom_bijectiveₓ'. -/
 theorem IsAlgebraic.algHom_bijective (ha : Algebra.IsAlgebraic K L) (f : L →ₐ[K] L) :
     Function.Bijective f :=
   by
@@ -416,21 +296,12 @@ theorem IsAlgebraic.algHom_bijective (ha : Algebra.IsAlgebraic K L) (f : L →
   exact ⟨a, Subtype.ext_iff.1 ha⟩
 #align algebra.is_algebraic.alg_hom_bijective Algebra.IsAlgebraic.algHom_bijective
 
-/- warning: alg_hom.bijective -> AlgHom.bijective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align alg_hom.bijective AlgHom.bijectiveₓ'. -/
 theorem AlgHom.bijective [FiniteDimensional K L] (ϕ : L →ₐ[K] L) : Function.Bijective ϕ :=
   (Algebra.isAlgebraic_of_finite K L).algHom_bijective ϕ
 #align alg_hom.bijective AlgHom.bijective
 
 variable (K L)
 
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-Case conversion may be inaccurate. Consider using '#align algebra.is_algebraic.alg_equiv_equiv_alg_hom Algebra.IsAlgebraic.algEquivEquivAlgHomₓ'. -/
 /-- Bijection between algebra equivalences and algebra homomorphisms -/
 @[simps]
 noncomputable def IsAlgebraic.algEquivEquivAlgHom (ha : Algebra.IsAlgebraic K L) :
@@ -442,12 +313,6 @@ noncomputable def IsAlgebraic.algEquivEquivAlgHom (ha : Algebra.IsAlgebraic K L)
   map_mul' _ _ := rfl
 #align algebra.is_algebraic.alg_equiv_equiv_alg_hom Algebra.IsAlgebraic.algEquivEquivAlgHom
 
-/- warning: alg_equiv_equiv_alg_hom -> algEquivEquivAlgHom is a dubious translation:
-lean 3 declaration is
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-  forall (K : Type.{u1}) (L : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_6 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] [_inst_14 : FiniteDimensional.{u1, u2} K L (Field.toDivisionRing.{u1} K _inst_1) (Ring.toAddCommGroup.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6)], MulEquiv.{u2, u2} (AlgEquiv.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6 _inst_6) (AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6 _inst_6) (MulOneClass.toMul.{u2} (AlgEquiv.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6 _inst_6) (Monoid.toMulOneClass.{u2} (AlgEquiv.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6 _inst_6) (DivInvMonoid.toMonoid.{u2} (AlgEquiv.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6 _inst_6) (Group.toDivInvMonoid.{u2} (AlgEquiv.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6 _inst_6) (AlgEquiv.aut.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6))))) (MulOneClass.toMul.{u2} (AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6 _inst_6) (Monoid.toMulOneClass.{u2} (AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6 _inst_6) (AlgHom.End.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6)))
-Case conversion may be inaccurate. Consider using '#align alg_equiv_equiv_alg_hom algEquivEquivAlgHomₓ'. -/
 /-- Bijection between algebra equivalences and algebra homomorphisms -/
 @[reducible]
 noncomputable def algEquivEquivAlgHom [FiniteDimensional K L] : (L ≃ₐ[K] L) ≃* (L →ₐ[K] L) :=
@@ -458,9 +323,6 @@ end Algebra
 
 variable {R S : Type _} [CommRing R] [IsDomain R] [CommRing S]
 
-/- warning: exists_integral_multiple -> exists_integral_multiple is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align exists_integral_multiple exists_integral_multipleₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y «expr ≠ » (0 : R)) -/
 theorem exists_integral_multiple [Algebra R S] {z : S} (hz : IsAlgebraic R z)
     (inj : ∀ x, algebraMap R S x = 0 → x = 0) :
@@ -476,9 +338,6 @@ theorem exists_integral_multiple [Algebra R S] {z : S} (hz : IsAlgebraic R z)
   exact ⟨⟨_, x_integral⟩, a, a_ne_zero, rfl⟩
 #align exists_integral_multiple exists_integral_multiple
 
-/- warning: is_integral_closure.exists_smul_eq_mul -> IsIntegralClosure.exists_smul_eq_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_integral_closure.exists_smul_eq_mul IsIntegralClosure.exists_smul_eq_mulₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (d «expr ≠ » (0 : R)) -/
 /-- A fraction `(a : S) / (b : S)` can be reduced to `(c : S) / (d : R)`,
 if `S` is the integral closure of `R` in an algebraic extension `L` of `R`. -/
@@ -502,9 +361,6 @@ section Field
 
 variable {K L : Type _} [Field K] [Field L] [Algebra K L] (A : Subalgebra K L)
 
-/- warning: inv_eq_of_aeval_div_X_ne_zero -> inv_eq_of_aeval_divX_ne_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align inv_eq_of_aeval_div_X_ne_zero inv_eq_of_aeval_divX_ne_zeroₓ'. -/
 theorem inv_eq_of_aeval_divX_ne_zero {x : L} {p : K[X]} (aeval_ne : aeval x (divX p) ≠ 0) :
     x⁻¹ = aeval x (divX p) / (aeval x p - algebraMap _ _ (p.coeff 0)) :=
   by
@@ -514,9 +370,6 @@ theorem inv_eq_of_aeval_divX_ne_zero {x : L} {p : K[X]} (aeval_ne : aeval x (div
   exact aeval_ne
 #align inv_eq_of_aeval_div_X_ne_zero inv_eq_of_aeval_divX_ne_zero
 
-/- warning: inv_eq_of_root_of_coeff_zero_ne_zero -> inv_eq_of_root_of_coeff_zero_ne_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align inv_eq_of_root_of_coeff_zero_ne_zero inv_eq_of_root_of_coeff_zero_ne_zeroₓ'. -/
 theorem inv_eq_of_root_of_coeff_zero_ne_zero {x : L} {p : K[X]} (aeval_eq : aeval x p = 0)
     (coeff_zero_ne : p.coeff 0 ≠ 0) : x⁻¹ = -(aeval x (divX p) / algebraMap _ _ (p.coeff 0)) :=
   by
@@ -528,9 +381,6 @@ theorem inv_eq_of_root_of_coeff_zero_ne_zero {x : L} {p : K[X]} (aeval_eq : aeva
   rw [AlgHom.map_add, AlgHom.map_mul, h, MulZeroClass.zero_mul, zero_add, aeval_C]
 #align inv_eq_of_root_of_coeff_zero_ne_zero inv_eq_of_root_of_coeff_zero_ne_zero
 
-/- warning: subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero -> Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zeroₓ'. -/
 theorem Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero {x : A} {p : K[X]}
     (aeval_eq : aeval x p = 0) (coeff_zero_ne : p.coeff 0 ≠ 0) : (x⁻¹ : L) ∈ A :=
   by
@@ -541,9 +391,6 @@ theorem Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero {x : A} {p : K[X]}
     map_inv₀, map_neg, inv_neg, neg_mul, Subalgebra.aeval_coe]
 #align subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero
 
-/- warning: subalgebra.inv_mem_of_algebraic -> Subalgebra.inv_mem_of_algebraic is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align subalgebra.inv_mem_of_algebraic Subalgebra.inv_mem_of_algebraicₓ'. -/
 theorem Subalgebra.inv_mem_of_algebraic {x : A} (hx : IsAlgebraic K (x : L)) : (x⁻¹ : L) ∈ A :=
   by
   obtain ⟨p, ne_zero, aeval_eq⟩ := hx
@@ -563,12 +410,6 @@ theorem Subalgebra.inv_mem_of_algebraic {x : A} (hx : IsAlgebraic K (x : L)) : (
       exact A.zero_mem
 #align subalgebra.inv_mem_of_algebraic Subalgebra.inv_mem_of_algebraic
 
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-Case conversion may be inaccurate. Consider using '#align subalgebra.is_field_of_algebraic Subalgebra.isField_of_algebraicₓ'. -/
 /-- In an algebraic extension L/K, an intermediate subalgebra is a field. -/
 theorem Subalgebra.isField_of_algebraic (hKL : Algebra.IsAlgebraic K L) : IsField A :=
   { show Nontrivial A by infer_instance, Subalgebra.toCommRing A with
@@ -646,21 +487,12 @@ noncomputable def Polynomial.algebraPi : Algebra R'[X] (S' → T') :=
 
 attribute [local instance] Polynomial.algebraPi
 
-/- warning: polynomial.algebra_map_pi_eq_aeval -> Polynomial.algebraMap_pi_eq_aeval is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.algebra_map_pi_eq_aeval Polynomial.algebraMap_pi_eq_aevalₓ'. -/
 @[simp]
 theorem Polynomial.algebraMap_pi_eq_aeval :
     (algebraMap R'[X] (S' → T') : R'[X] → S' → T') = fun p z => algebraMap _ _ (aeval z p) :=
   rfl
 #align polynomial.algebra_map_pi_eq_aeval Polynomial.algebraMap_pi_eq_aeval
 
-/- warning: polynomial.algebra_map_pi_self_eq_eval -> Polynomial.algebraMap_pi_self_eq_eval is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align polynomial.algebra_map_pi_self_eq_eval Polynomial.algebraMap_pi_self_eq_evalₓ'. -/
 @[simp]
 theorem Polynomial.algebraMap_pi_self_eq_eval :
     (algebraMap R'[X] (R' → R') : R'[X] → R' → R') = fun p z => eval z p :=

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

@@ -160,9 +160,7 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3)] [_inst_8 : Nontrivial.{u1} R], IsAlgebraic.{u1, u2} R A _inst_1 _inst_3 _inst_4 (OfNat.ofNat.{u2} A 1 (One.toOfNat1.{u2} A (Semiring.toOne.{u2} A (Ring.toSemiring.{u2} A _inst_3))))
 Case conversion may be inaccurate. Consider using '#align is_algebraic_one isAlgebraic_oneₓ'. -/
-theorem isAlgebraic_one [Nontrivial R] : IsAlgebraic R (1 : A) :=
-  by
-  rw [← _root_.map_one _]
+theorem isAlgebraic_one [Nontrivial R] : IsAlgebraic R (1 : A) := by rw [← _root_.map_one _];
   exact isAlgebraic_algebraMap 1
 #align is_algebraic_one isAlgebraic_one
 
@@ -172,9 +170,7 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3)] [_inst_8 : Nontrivial.{u1} R] (n : Nat), IsAlgebraic.{u1, u2} R A _inst_1 _inst_3 _inst_4 (Nat.cast.{u2} A (Semiring.toNatCast.{u2} A (Ring.toSemiring.{u2} A _inst_3)) n)
 Case conversion may be inaccurate. Consider using '#align is_algebraic_nat isAlgebraic_natₓ'. -/
-theorem isAlgebraic_nat [Nontrivial R] (n : ℕ) : IsAlgebraic R (n : A) :=
-  by
-  rw [← map_natCast _]
+theorem isAlgebraic_nat [Nontrivial R] (n : ℕ) : IsAlgebraic R (n : A) := by rw [← map_natCast _];
   exact isAlgebraic_algebraMap n
 #align is_algebraic_nat isAlgebraic_nat
 
@@ -184,10 +180,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3)] [_inst_8 : Nontrivial.{u1} R] (n : Int), IsAlgebraic.{u1, u2} R A _inst_1 _inst_3 _inst_4 (Int.cast.{u2} A (Ring.toIntCast.{u2} A _inst_3) n)
 Case conversion may be inaccurate. Consider using '#align is_algebraic_int isAlgebraic_intₓ'. -/
-theorem isAlgebraic_int [Nontrivial R] (n : ℤ) : IsAlgebraic R (n : A) :=
-  by
-  rw [← _root_.map_int_cast (algebraMap R A)]
-  exact isAlgebraic_algebraMap n
+theorem isAlgebraic_int [Nontrivial R] (n : ℤ) : IsAlgebraic R (n : A) := by
+  rw [← _root_.map_int_cast (algebraMap R A)]; exact isAlgebraic_algebraMap n
 #align is_algebraic_int isAlgebraic_int
 
 /- warning: is_algebraic_rat -> isAlgebraic_rat is a dubious translation:
@@ -197,9 +191,7 @@ but is expected to have type
   forall (R : Type.{u1}) {A : Type.{u2}} [_inst_8 : DivisionRing.{u2} A] [_inst_9 : Field.{u1} R] [_inst_10 : Algebra.{u1, u2} R A (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_9)) (DivisionSemiring.toSemiring.{u2} A (DivisionRing.toDivisionSemiring.{u2} A _inst_8))] (n : Rat), IsAlgebraic.{u1, u2} R A (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R _inst_9)) (DivisionRing.toRing.{u2} A _inst_8) _inst_10 (Rat.cast.{u2} A (DivisionRing.toRatCast.{u2} A _inst_8) n)
 Case conversion may be inaccurate. Consider using '#align is_algebraic_rat isAlgebraic_ratₓ'. -/
 theorem isAlgebraic_rat (R : Type u) {A : Type v} [DivisionRing A] [Field R] [Algebra R A] (n : ℚ) :
-    IsAlgebraic R (n : A) := by
-  rw [← map_ratCast (algebraMap R A)]
-  exact isAlgebraic_algebraMap n
+    IsAlgebraic R (n : A) := by rw [← map_ratCast (algebraMap R A)]; exact isAlgebraic_algebraMap n
 #align is_algebraic_rat isAlgebraic_rat
 
 #print isAlgebraic_of_mem_rootSet /-
@@ -445,12 +437,8 @@ noncomputable def IsAlgebraic.algEquivEquivAlgHom (ha : Algebra.IsAlgebraic K L)
     (L ≃ₐ[K] L) ≃* (L →ₐ[K] L) where
   toFun ϕ := ϕ.toAlgHom
   invFun ϕ := AlgEquiv.ofBijective ϕ (ha.algHom_bijective ϕ)
-  left_inv _ := by
-    ext
-    rfl
-  right_inv _ := by
-    ext
-    rfl
+  left_inv _ := by ext; rfl
+  right_inv _ := by ext; rfl
   map_mul' _ _ := rfl
 #align algebra.is_algebraic.alg_equiv_equiv_alg_hom Algebra.IsAlgebraic.algEquivEquivAlgHom
 
@@ -546,9 +534,7 @@ Case conversion may be inaccurate. Consider using '#align subalgebra.inv_mem_of_
 theorem Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero {x : A} {p : K[X]}
     (aeval_eq : aeval x p = 0) (coeff_zero_ne : p.coeff 0 ≠ 0) : (x⁻¹ : L) ∈ A :=
   by
-  suffices (x⁻¹ : L) = (-p.coeff 0)⁻¹ • aeval x (div_X p)
-    by
-    rw [this]
+  suffices (x⁻¹ : L) = (-p.coeff 0)⁻¹ • aeval x (div_X p) by rw [this];
     exact A.smul_mem (aeval x _).2 _
   have : aeval (x : L) p = 0 := by rw [Subalgebra.aeval_coe, aeval_eq, Subalgebra.coe_zero]
   rw [inv_eq_of_root_of_coeff_zero_ne_zero this coeff_zero_ne, div_eq_inv_mul, Algebra.smul_def,

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

@@ -212,10 +212,7 @@ theorem isAlgebraic_of_mem_rootSet {R : Type u} {A : Type v} [Field R] [Field A]
 open IsScalarTower
 
 /- warning: is_algebraic_algebra_map_of_is_algebraic -> isAlgebraic_algebraMap_of_isAlgebraic is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {S : Type.{u3}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u3} S] [_inst_3 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u3} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))] [_inst_6 : Algebra.{u3, u2} S A (CommRing.toCommSemiring.{u3} S _inst_2) (Ring.toSemiring.{u2} A _inst_3)] [_inst_7 : IsScalarTower.{u1, u3, u2} R S A (SMulZeroClass.toHasSmul.{u1, u3} R S (AddZeroClass.toHasZero.{u3} S (AddMonoid.toAddZeroClass.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} S (AddMonoid.toAddZeroClass.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} S (AddMonoid.toAddZeroClass.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u3} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))))) (Algebra.toModule.{u1, u3} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u2} S A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_3))))))) (SMulWithZero.toSmulZeroClass.{u3, u2} S A (MulZeroClass.toHasZero.{u3} S (MulZeroOneClass.toMulZeroClass.{u3} S (MonoidWithZero.toMulZeroOneClass.{u3} S (Semiring.toMonoidWithZero.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_3))))))) (MulActionWithZero.toSMulWithZero.{u3, u2} S A (Semiring.toMonoidWithZero.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_3))))))) (Module.toMulActionWithZero.{u3, u2} S A (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_3)))) (Algebra.toModule.{u3, u2} S A 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(Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_3))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_3)))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3) _inst_4)))))] {a : S}, (IsAlgebraic.{u1, u3} R S _inst_1 (CommRing.toRing.{u3} S _inst_2) _inst_5 a) -> (IsAlgebraic.{u1, u2} R A _inst_1 _inst_3 _inst_4 (coeFn.{max (succ u3) (succ u2), max (succ u3) (succ u2)} 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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_algebraic_algebra_map_of_is_algebraic isAlgebraic_algebraMap_of_isAlgebraicₓ'. -/
 theorem isAlgebraic_algebraMap_of_isAlgebraic {a : S} :
     IsAlgebraic R a → IsAlgebraic R (algebraMap S A a) := fun ⟨f, hf₁, hf₂⟩ =>
@@ -223,10 +220,7 @@ theorem isAlgebraic_algebraMap_of_isAlgebraic {a : S} :
 #align is_algebraic_algebra_map_of_is_algebraic isAlgebraic_algebraMap_of_isAlgebraic
 
 /- warning: is_algebraic_alg_hom_of_is_algebraic -> isAlgebraic_algHom_of_isAlgebraic is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_algebraic_alg_hom_of_is_algebraic isAlgebraic_algHom_of_isAlgebraicₓ'. -/
 /-- This is slightly more general than `is_algebraic_algebra_map_of_is_algebraic` in that it
   allows noncommutative intermediate rings `A`. -/
@@ -260,10 +254,7 @@ theorem AlgEquiv.isAlgebraic_iff {B} [Ring B] [Algebra R B] (e : A ≃ₐ[R] B)
 #align alg_equiv.is_algebraic_iff AlgEquiv.isAlgebraic_iff
 
 /- warning: is_algebraic_algebra_map_iff -> isAlgebraic_algebraMap_iff is a dubious translation:
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(RingHom.{u1, u3} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_3))) S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_3)) (RingHom.instRingHomClassRingHom.{u1, u3} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_3)))))) (algebraMap.{u1, u3} S A (CommRing.toCommSemiring.{u1} S _inst_2) (Ring.toSemiring.{u3} A _inst_3) _inst_6) a)) (IsAlgebraic.{u2, u1} R S _inst_1 (CommRing.toRing.{u1} S _inst_2) _inst_5 a))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_algebraic_algebra_map_iff isAlgebraic_algebraMap_iffₓ'. -/
 theorem isAlgebraic_algebraMap_iff {a : S} (h : Function.Injective (algebraMap S A)) :
     IsAlgebraic R (algebraMap S A a) ↔ IsAlgebraic R a :=
@@ -348,10 +339,7 @@ theorem isAlgebraic_trans (L_alg : IsAlgebraic K L) (A_alg : IsAlgebraic L A) :
 variable (K L)
 
 /- warning: is_algebraic_of_larger_base_of_injective -> isAlgebraic_of_larger_base_of_injective is a dubious translation:
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_inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_10))) -> (forall {x : A}, (IsAlgebraic.{u1, u3} R A _inst_3 (CommRing.toRing.{u3} A _inst_5) _inst_12 x) -> (IsAlgebraic.{u2, u3} S A _inst_4 (CommRing.toRing.{u3} A _inst_5) _inst_11 x))
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_algebraic_of_larger_base_of_injective isAlgebraic_of_larger_base_of_injectiveₓ'. -/
 /-- If x is algebraic over R, then x is algebraic over S when S is an extension of R,
   and the map from `R` to `S` is injective. -/
@@ -363,10 +351,7 @@ theorem isAlgebraic_of_larger_base_of_injective (hinj : Function.Injective (alge
 #align is_algebraic_of_larger_base_of_injective isAlgebraic_of_larger_base_of_injective
 
 /- warning: algebra.is_algebraic_of_larger_base_of_injective -> Algebra.isAlgebraic_of_larger_base_of_injective is a dubious translation:
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(MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_10))))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (Module.toMulActionWithZero.{u2, u3} S A (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))))) (Algebra.toModule.{u2, u3} S A (CommRing.toCommSemiring.{u2} S _inst_4) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)) _inst_11))))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_3) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)) _inst_12)))))], (Function.Injective.{succ u1, succ u2} R S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_10))) -> (Algebra.IsAlgebraic.{u1, u3} R A _inst_3 (CommRing.toRing.{u3} A _inst_5) _inst_12) -> (Algebra.IsAlgebraic.{u2, u3} S A _inst_4 (CommRing.toRing.{u3} A _inst_5) _inst_11)
-but is expected to have type
-  forall {R : Type.{u3}} {S : Type.{u2}} {A : Type.{u1}} [_inst_3 : CommRing.{u3} R] [_inst_4 : CommRing.{u2} S] [_inst_5 : CommRing.{u1} A] [_inst_10 : Algebra.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))] [_inst_11 : Algebra.{u2, u1} S A (CommRing.toCommSemiring.{u2} S _inst_4) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))] [_inst_12 : Algebra.{u3, u1} R A (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))] [_inst_13 : IsScalarTower.{u3, u2, u1} R S A (Algebra.toSMul.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) _inst_10) (Algebra.toSMul.{u2, u1} S A (CommRing.toCommSemiring.{u2} S _inst_4) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)) _inst_11) (Algebra.toSMul.{u3, u1} R A (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)) _inst_12)], (Function.Injective.{succ u3, succ u2} R S (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))) R S (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))) R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))) (RingHom.instRingHomClassRingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))))) (algebraMap.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) _inst_10))) -> (Algebra.IsAlgebraic.{u3, u1} R A _inst_3 (CommRing.toRing.{u1} A _inst_5) _inst_12) -> (Algebra.IsAlgebraic.{u2, u1} S A _inst_4 (CommRing.toRing.{u1} A _inst_5) _inst_11)
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebra.is_algebraic_of_larger_base_of_injective Algebra.isAlgebraic_of_larger_base_of_injectiveₓ'. -/
 /-- If A is an algebraic algebra over R, then A is algebraic over S when S is an extension of R,
   and the map from `R` to `S` is injective. -/
@@ -424,10 +409,7 @@ theorem isAlgebraic_of_finite [finite : FiniteDimensional K L] : IsAlgebraic K L
 variable {K L}
 
 /- warning: algebra.is_algebraic.alg_hom_bijective -> Algebra.IsAlgebraic.algHom_bijective is a dubious translation:
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(DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6))))) (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u2, u1, u1} (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) K L L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u2, u1, u1} (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) K L L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u1, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6 (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) (AlgHom.algHomClass.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6))))) f))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebra.is_algebraic.alg_hom_bijective Algebra.IsAlgebraic.algHom_bijectiveₓ'. -/
 theorem IsAlgebraic.algHom_bijective (ha : Algebra.IsAlgebraic K L) (f : L →ₐ[K] L) :
     Function.Bijective f :=
@@ -443,10 +425,7 @@ theorem IsAlgebraic.algHom_bijective (ha : Algebra.IsAlgebraic K L) (f : L →
 #align algebra.is_algebraic.alg_hom_bijective Algebra.IsAlgebraic.algHom_bijective
 
 /- warning: alg_hom.bijective -> AlgHom.bijective is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_6 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_14 : FiniteDimensional.{u1, u2} K L (Field.toDivisionRing.{u1} K _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6)] (ϕ : AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6), Function.Bijective.{succ u2, succ u2} L L (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) (fun (_x : AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) => L -> L) ([anonymous].{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) ϕ)
-but is expected to have type
-  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_6 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] [_inst_14 : FiniteDimensional.{u2, u1} K L (Field.toDivisionRing.{u2} K _inst_1) (Ring.toAddCommGroup.{u1} L (DivisionRing.toRing.{u1} L (Field.toDivisionRing.{u1} L _inst_2))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)] (ϕ : AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L 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(Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) (AlgHom.algHomClass.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6))))) ϕ)
+<too large>
 Case conversion may be inaccurate. Consider using '#align alg_hom.bijective AlgHom.bijectiveₓ'. -/
 theorem AlgHom.bijective [FiniteDimensional K L] (ϕ : L →ₐ[K] L) : Function.Bijective ϕ :=
   (Algebra.isAlgebraic_of_finite K L).algHom_bijective ϕ
@@ -492,10 +471,7 @@ end Algebra
 variable {R S : Type _} [CommRing R] [IsDomain R] [CommRing S]
 
 /- warning: exists_integral_multiple -> exists_integral_multiple is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align exists_integral_multiple exists_integral_multipleₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y «expr ≠ » (0 : R)) -/
 theorem exists_integral_multiple [Algebra R S] {z : S} (hz : IsAlgebraic R z)
@@ -513,10 +489,7 @@ theorem exists_integral_multiple [Algebra R S] {z : S} (hz : IsAlgebraic R z)
 #align exists_integral_multiple exists_integral_multiple
 
 /- warning: is_integral_closure.exists_smul_eq_mul -> IsIntegralClosure.exists_smul_eq_mul is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : CommRing.{u2} S] {L : Type.{u3}} [_inst_4 : Field.{u3} L] [_inst_5 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3))] [_inst_6 : Algebra.{u2, u3} S L (CommRing.toCommSemiring.{u2} S _inst_3) (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4)))] [_inst_7 : Algebra.{u1, u3} R L (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4)))] [_inst_8 : IsScalarTower.{u1, u2, u3} R S L (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3)) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u3} S L (AddZeroClass.toHasZero.{u3} L (AddMonoid.toAddZeroClass.{u3} L (AddCommMonoid.toAddMonoid.{u3} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L (Semiring.toNonAssocSemiring.{u3} L (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4))))))))) 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(Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4))))))))) (Module.toMulActionWithZero.{u2, u3} S L (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L (Semiring.toNonAssocSemiring.{u3} L (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4)))))) (Algebra.toModule.{u2, u3} S L (CommRing.toCommSemiring.{u2} S _inst_3) (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4))) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} R L (AddZeroClass.toHasZero.{u3} L (AddMonoid.toAddZeroClass.{u3} L (AddCommMonoid.toAddMonoid.{u3} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L (Semiring.toNonAssocSemiring.{u3} L (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4))))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R L (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} L (AddMonoid.toAddZeroClass.{u3} L (AddCommMonoid.toAddMonoid.{u3} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L (Semiring.toNonAssocSemiring.{u3} L (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4))))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R L (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} L (AddMonoid.toAddZeroClass.{u3} L (AddCommMonoid.toAddMonoid.{u3} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L (Semiring.toNonAssocSemiring.{u3} L (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4))))))))) (Module.toMulActionWithZero.{u1, u3} R L (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L (Semiring.toNonAssocSemiring.{u3} L (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4)))))) (Algebra.toModule.{u1, u3} R L (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4))) _inst_7)))))] [_inst_9 : IsIntegralClosure.{u2, u1, u3} S R L _inst_1 (CommRing.toCommSemiring.{u2} S _inst_3) (EuclideanDomain.toCommRing.{u3} L (Field.toEuclideanDomain.{u3} L _inst_4)) _inst_7 _inst_6], (Algebra.IsAlgebraic.{u1, u3} R L _inst_1 (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4)) _inst_7) -> (Function.Injective.{succ u1, succ u3} R L (coeFn.{max (succ 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(Field.toDivisionRing.{u3} L _inst_4))) _inst_7))) -> (forall (a : S) {b : S}, (Ne.{succ u2} S b (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_3)))))))))) -> (Exists.{succ u2} S (fun (c : S) => Exists.{succ u1} R (fun (d : R) => Exists.{0} (Ne.{succ u1} R d (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))) (fun (H : Ne.{succ u1} R d (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))) => Eq.{succ u2} S (SMul.smul.{u1, u2} R S (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3)) _inst_5))))) d a) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (Ring.toDistrib.{u2} S (CommRing.toRing.{u2} S _inst_3)))) b c))))))
-but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : IsDomain.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))] [_inst_3 : CommRing.{u1} S] {L : Type.{u3}} [_inst_4 : Field.{u3} L] [_inst_5 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3))] [_inst_6 : Algebra.{u1, u3} S L (CommRing.toCommSemiring.{u1} S _inst_3) (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_4)))] [_inst_7 : Algebra.{u2, u3} R L (CommRing.toCommSemiring.{u2} R _inst_1) (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_4)))] [_inst_8 : IsScalarTower.{u2, u1, u3} R S L (Algebra.toSMul.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)) _inst_5) (Algebra.toSMul.{u1, u3} S L (CommRing.toCommSemiring.{u1} S _inst_3) (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_4))) _inst_6) (Algebra.toSMul.{u2, u3} R L (CommRing.toCommSemiring.{u2} R _inst_1) (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_4))) _inst_7)] [_inst_9 : IsIntegralClosure.{u1, u2, u3} S R L _inst_1 (CommRing.toCommSemiring.{u1} S _inst_3) (EuclideanDomain.toCommRing.{u3} L (Field.toEuclideanDomain.{u3} L _inst_4)) _inst_7 _inst_6], (Algebra.IsAlgebraic.{u2, u3} R L _inst_1 (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4)) _inst_7) -> (Function.Injective.{succ u2, succ u3} R L (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R L (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} L (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_4))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => L) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R L (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} L (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_4))))) R L (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u3} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L (Semiring.toNonAssocSemiring.{u3} L (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_4)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R L (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} L (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_4))))) R L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L (Semiring.toNonAssocSemiring.{u3} L (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_4))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R L (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} L (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_4))))) R L (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} L (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_4)))) (RingHom.instRingHomClassRingHom.{u2, u3} R L (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} L (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_4)))))))) (algebraMap.{u2, u3} R L (CommRing.toCommSemiring.{u2} R _inst_1) (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_4))) _inst_7))) -> (forall (a : S) {b : S}, (Ne.{succ u1} S b (OfNat.ofNat.{u1} S 0 (Zero.toOfNat0.{u1} S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)))))) -> (Exists.{succ u1} S (fun (c : S) => Exists.{succ u2} R (fun (d : R) => Exists.{0} (Ne.{succ u2} R d (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} R (IsDomain.toCancelCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1) _inst_2)))))) (fun (H : Ne.{succ u2} R d (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} R (IsDomain.toCancelCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1) _inst_2)))))) => Eq.{succ u1} S (HSMul.hSMul.{u2, u1, u1} R S S (instHSMul.{u2, u1} R S (Algebra.toSMul.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)) _inst_5)) d a) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_3))))) b c))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_integral_closure.exists_smul_eq_mul IsIntegralClosure.exists_smul_eq_mulₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (d «expr ≠ » (0 : R)) -/
 /-- A fraction `(a : S) / (b : S)` can be reduced to `(c : S) / (d : R)`,
@@ -542,10 +515,7 @@ section Field
 variable {K L : Type _} [Field K] [Field L] [Algebra K L] (A : Subalgebra K L)
 
 /- warning: inv_eq_of_aeval_div_X_ne_zero -> inv_eq_of_aeval_divX_ne_zero is a dubious translation:
-lean 3 declaration is
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(Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))))) (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6 (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6))))) (Polynomial.aeval.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6 x) (Polynomial.divX.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) (Polynomial.divX.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) (Polynomial.divX.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p)) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) (Polynomial.divX.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p)) (CommGroupWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) (Polynomial.divX.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p)) (Semifield.toCommGroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) (Polynomial.divX.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) (Polynomial.divX.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p)) _inst_5))))))) -> (Eq.{succ u1} L (Inv.inv.{u1} L (Field.toInv.{u1} L _inst_5) x) (HDiv.hDiv.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) (Polynomial.divX.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p)) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) p) L (instHDiv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) (Polynomial.divX.{u2} 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(Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 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(Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6 (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K 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=> L) p) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) p) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) p) _inst_5)))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K 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(Field.toSemifield.{u2} K _inst_4)))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))))) (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6 (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6))))) (Polynomial.aeval.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6 x) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (RingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) K L (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (NonUnitalNonAssocSemiring.toMul.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L 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+<too large>
 Case conversion may be inaccurate. Consider using '#align inv_eq_of_aeval_div_X_ne_zero inv_eq_of_aeval_divX_ne_zeroₓ'. -/
 theorem inv_eq_of_aeval_divX_ne_zero {x : L} {p : K[X]} (aeval_ne : aeval x (divX p) ≠ 0) :
     x⁻¹ = aeval x (divX p) / (aeval x p - algebraMap _ _ (p.coeff 0)) :=
@@ -557,10 +527,7 @@ theorem inv_eq_of_aeval_divX_ne_zero {x : L} {p : K[X]} (aeval_ne : aeval x (div
 #align inv_eq_of_aeval_div_X_ne_zero inv_eq_of_aeval_divX_ne_zero
 
 /- warning: inv_eq_of_root_of_coeff_zero_ne_zero -> inv_eq_of_root_of_coeff_zero_ne_zero is a dubious translation:
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(Field.toSemifield.{u2} K _inst_4)))) (AddMonoid.toZero.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))))) (DistribSMul.toSMulZeroClass.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))))) (DistribMulAction.toDistribSMul.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))))) (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6 (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6))))) (Polynomial.aeval.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6 x) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K 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(x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) p) _inst_5))))))) -> (Ne.{succ u2} K (Polynomial.coeff.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (OfNat.ofNat.{u2} K 0 (Zero.toOfNat0.{u2} K (CommMonoidWithZero.toZero.{u2} K (CommGroupWithZero.toCommMonoidWithZero.{u2} K (Semifield.toCommGroupWithZero.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) -> (Eq.{succ u1} L (Inv.inv.{u1} L (Field.toInv.{u1} L _inst_5) x) (Neg.neg.{u1} L (Ring.toNeg.{u1} L (DivisionRing.toRing.{u1} L (Field.toDivisionRing.{u1} L _inst_5))) (HDiv.hDiv.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) (Polynomial.divX.{u2} K 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_inst_4))) p)) _inst_5)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (fun (_x : Polynomial.{u2} 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(CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))))) (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K 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(Field.toSemifield.{u1} L _inst_5))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))))) 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_inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} 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(CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K 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(Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K 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+<too large>
 Case conversion may be inaccurate. Consider using '#align inv_eq_of_root_of_coeff_zero_ne_zero inv_eq_of_root_of_coeff_zero_ne_zeroₓ'. -/
 theorem inv_eq_of_root_of_coeff_zero_ne_zero {x : L} {p : K[X]} (aeval_eq : aeval x p = 0)
     (coeff_zero_ne : p.coeff 0 ≠ 0) : x⁻¹ = -(aeval x (divX p) / algebraMap _ _ (p.coeff 0)) :=
@@ -574,10 +541,7 @@ theorem inv_eq_of_root_of_coeff_zero_ne_zero {x : L} {p : K[X]} (aeval_eq : aeva
 #align inv_eq_of_root_of_coeff_zero_ne_zero inv_eq_of_root_of_coeff_zero_ne_zero
 
 /- warning: subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero -> Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero is a dubious translation:
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(Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))))))) (Module.toDistribMulAction.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) 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(Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))))))) (SMulZeroClass.toSMul.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (AddMonoid.toZero.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)))))) (DistribSMul.toSMulZeroClass.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)))))) (DistribMulAction.toDistribSMul.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)))) (Algebra.toModule.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)) K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A))))) (Module.toDistribMulAction.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))))) (Algebra.toModule.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)))) (Algebra.toModule.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)) K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A))) (Module.toDistribMulAction.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))))) (Algebra.toModule.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)))) (Algebra.toModule.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K 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(Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) 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K (Field.toSemifield.{u1} K _inst_4)))) => Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) p) (ZeroMemClass.zero.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (CommMonoidWithZero.toZero.{u2} L (CommGroupWithZero.toCommMonoidWithZero.{u2} L (Semifield.toCommGroupWithZero.{u2} L (Field.toSemifield.{u2} L _inst_5)))) (AddSubmonoidClass.toZeroMemClass.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (AddMonoid.toAddZeroClass.{u2} L (AddMonoidWithOne.toAddMonoid.{u2} L (AddGroupWithOne.toAddMonoidWithOne.{u2} L (Ring.toAddGroupWithOne.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5)))))) (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L 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(Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6))) A)))) -> (Ne.{succ u1} K (Polynomial.coeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) p (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_4))))))) -> (Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) (Inv.inv.{u2} L (Field.toInv.{u2} L _inst_5) (Subtype.val.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Set.{u2} L) (Set.instMembershipSet.{u2} L) x (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) A)) x)) A)
+<too large>
 Case conversion may be inaccurate. Consider using '#align subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zeroₓ'. -/
 theorem Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero {x : A} {p : K[X]}
     (aeval_eq : aeval x p = 0) (coeff_zero_ne : p.coeff 0 ≠ 0) : (x⁻¹ : L) ∈ A :=
@@ -592,10 +556,7 @@ theorem Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero {x : A} {p : K[X]}
 #align subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero
 
 /- warning: subalgebra.inv_mem_of_algebraic -> Subalgebra.inv_mem_of_algebraic is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align subalgebra.inv_mem_of_algebraic Subalgebra.inv_mem_of_algebraicₓ'. -/
 theorem Subalgebra.inv_mem_of_algebraic {x : A} (hx : IsAlgebraic K (x : L)) : (x⁻¹ : L) ∈ A :=
   by
@@ -700,10 +661,7 @@ noncomputable def Polynomial.algebraPi : Algebra R'[X] (S' → T') :=
 attribute [local instance] Polynomial.algebraPi
 
 /- warning: polynomial.algebra_map_pi_eq_aeval -> Polynomial.algebraMap_pi_eq_aeval is a dubious translation:
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(x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) _inst_5)) (Semiring.toNonAssocSemiring.{u3} T' (CommSemiring.toSemiring.{u3} T' _inst_6)))))) (algebraMap.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) T' _inst_5 (CommSemiring.toSemiring.{u3} T' _inst_6) _inst_8) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgHom.{u1, u1, u2} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) S' _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u2} S' _inst_5) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)) _inst_7) (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (fun (_x : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') _x) (SMulHomClass.toFunLike.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) S' _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u2} S' _inst_5) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)) _inst_7) R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) S' (SMulZeroClass.toSMul.{u1, u1} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (AddMonoid.toZero.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4))))))) (DistribMulAction.toDistribSMul.{u1, u1} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)))))) (Module.toDistribMulAction.{u1, u1} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} R' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4))))) (Algebra.toModule.{u1, u1} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4))))))) (SMulZeroClass.toSMul.{u1, u2} R' S' (AddMonoid.toZero.{u2} S' (AddCommMonoid.toAddMonoid.{u2} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S' (Semiring.toNonAssocSemiring.{u2} S' (CommSemiring.toSemiring.{u2} S' _inst_5)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R' S' (AddMonoid.toAddZeroClass.{u2} S' (AddCommMonoid.toAddMonoid.{u2} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S' (Semiring.toNonAssocSemiring.{u2} S' (CommSemiring.toSemiring.{u2} S' _inst_5)))))) (DistribMulAction.toDistribSMul.{u1, u2} R' S' (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4))) (AddCommMonoid.toAddMonoid.{u2} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S' (Semiring.toNonAssocSemiring.{u2} S' (CommSemiring.toSemiring.{u2} S' _inst_5))))) (Module.toDistribMulAction.{u1, u2} R' S' (CommSemiring.toSemiring.{u1} R' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S' (Semiring.toNonAssocSemiring.{u2} S' (CommSemiring.toSemiring.{u2} S' _inst_5)))) (Algebra.toModule.{u1, u2} R' S' _inst_4 (CommSemiring.toSemiring.{u2} S' _inst_5) _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) S' _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u2} S' _inst_5) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)) _inst_7) R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) S' (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)))))) (AddCommMonoid.toAddMonoid.{u2} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S' (Semiring.toNonAssocSemiring.{u2} S' (CommSemiring.toSemiring.{u2} S' _inst_5))))) (Module.toDistribMulAction.{u1, u1} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} R' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4))))) (Algebra.toModule.{u1, u1} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)))) (Module.toDistribMulAction.{u1, u2} R' S' (CommSemiring.toSemiring.{u1} R' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S' (Semiring.toNonAssocSemiring.{u2} S' (CommSemiring.toSemiring.{u2} S' _inst_5)))) (Algebra.toModule.{u1, u2} R' S' _inst_4 (CommSemiring.toSemiring.{u2} S' _inst_5) _inst_7)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) S' _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u2} S' _inst_5) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)) _inst_7) R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) S' (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S' (Semiring.toNonAssocSemiring.{u2} S' (CommSemiring.toSemiring.{u2} S' _inst_5))) (Module.toDistribMulAction.{u1, u1} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} R' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4))))) (Algebra.toModule.{u1, u1} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)))) (Module.toDistribMulAction.{u1, u2} R' S' (CommSemiring.toSemiring.{u1} R' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S' (Semiring.toNonAssocSemiring.{u2} S' (CommSemiring.toSemiring.{u2} S' _inst_5)))) (Algebra.toModule.{u1, u2} R' S' _inst_4 (CommSemiring.toSemiring.{u2} S' _inst_5) _inst_7)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) S' _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u2} S' _inst_5) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)) _inst_7 (AlgHom.{u1, u1, u2} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) S' _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u2} S' _inst_5) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)) _inst_7) (AlgHom.algHomClass.{u1, u1, u2} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) S' _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u2} S' _inst_5) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)) _inst_7))))) (Polynomial.aeval.{u1, u2} R' S' _inst_4 (CommSemiring.toSemiring.{u2} S' _inst_5) _inst_7 z) p))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.algebra_map_pi_eq_aeval Polynomial.algebraMap_pi_eq_aevalₓ'. -/
 @[simp]
 theorem Polynomial.algebraMap_pi_eq_aeval :

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

@@ -226,7 +226,7 @@ theorem isAlgebraic_algebraMap_of_isAlgebraic {a : S} :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3)] {B : Type.{u3}} [_inst_8 : Ring.{u3} B] [_inst_9 : Algebra.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B _inst_8)] (f : AlgHom.{u1, u2, u3} R A B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3) (Ring.toSemiring.{u3} B _inst_8) _inst_4 _inst_9) {a : A}, (IsAlgebraic.{u1, u2} R A _inst_1 _inst_3 _inst_4 a) -> (IsAlgebraic.{u1, u3} R B _inst_1 _inst_8 _inst_9 (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3) (Ring.toSemiring.{u3} B _inst_8) _inst_4 _inst_9) (fun (_x : AlgHom.{u1, u2, u3} R A B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3) (Ring.toSemiring.{u3} B _inst_8) _inst_4 _inst_9) => A -> B) ([anonymous].{u1, u2, u3} R A B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3) (Ring.toSemiring.{u3} B _inst_8) _inst_4 _inst_9) f a))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_3 : Ring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3)] {B : Type.{u1}} [_inst_8 : Ring.{u1} B] [_inst_9 : Algebra.{u2, u1} R B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} B _inst_8)] (f : AlgHom.{u2, u3, u1} R A B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3) (Ring.toSemiring.{u1} B _inst_8) _inst_4 _inst_9) {a : A}, (IsAlgebraic.{u2, u3} R A _inst_1 _inst_3 _inst_4 a) -> (IsAlgebraic.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) _inst_1 _inst_8 _inst_9 (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (AlgHom.{u2, u3, u1} R A B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3) (Ring.toSemiring.{u1} B _inst_8) _inst_4 _inst_9) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u3 u1, u2, u3, u1} (AlgHom.{u2, u3, u1} R A B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3) (Ring.toSemiring.{u1} B _inst_8) _inst_4 _inst_9) R A B (SMulZeroClass.toSMul.{u2, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_3)))))) (DistribSMul.toSMulZeroClass.{u2, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_3)))))) (DistribMulAction.toDistribSMul.{u2, u3} R A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_3))))) (Module.toDistribMulAction.{u2, u3} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_3)))) (Algebra.toModule.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3) _inst_4))))) (SMulZeroClass.toSMul.{u2, u1} R B (AddMonoid.toZero.{u1} B (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B _inst_8)))))) (DistribSMul.toSMulZeroClass.{u2, u1} R B (AddMonoid.toAddZeroClass.{u1} B (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B _inst_8)))))) (DistribMulAction.toDistribSMul.{u2, u1} R B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B _inst_8))))) (Module.toDistribMulAction.{u2, u1} R B (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B _inst_8)))) (Algebra.toModule.{u2, u1} R B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} B _inst_8) _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u1, u2, u3, u1} (AlgHom.{u2, u3, u1} R A B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3) (Ring.toSemiring.{u1} B _inst_8) _inst_4 _inst_9) R A B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_3))))) (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B _inst_8))))) (Module.toDistribMulAction.{u2, u3} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_3)))) (Algebra.toModule.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3) _inst_4)) (Module.toDistribMulAction.{u2, u1} R B (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B _inst_8)))) (Algebra.toModule.{u2, u1} R B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} B _inst_8) _inst_9)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u1, u2, u3, u1} (AlgHom.{u2, u3, u1} R A B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3) (Ring.toSemiring.{u1} B _inst_8) _inst_4 _inst_9) R A B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B _inst_8))) (Module.toDistribMulAction.{u2, u3} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_3)))) (Algebra.toModule.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3) _inst_4)) (Module.toDistribMulAction.{u2, u1} R B (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B _inst_8)))) (Algebra.toModule.{u2, u1} R B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} B _inst_8) _inst_9)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u1, max u3 u1} R A B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3) (Ring.toSemiring.{u1} B _inst_8) _inst_4 _inst_9 (AlgHom.{u2, u3, u1} R A B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3) (Ring.toSemiring.{u1} B _inst_8) _inst_4 _inst_9) (AlgHom.algHomClass.{u2, u3, u1} R A B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3) (Ring.toSemiring.{u1} B _inst_8) _inst_4 _inst_9))))) f a))
+  forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_3 : Ring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3)] {B : Type.{u1}} [_inst_8 : Ring.{u1} B] [_inst_9 : Algebra.{u2, u1} R B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} B _inst_8)] (f : AlgHom.{u2, u3, u1} R A B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3) (Ring.toSemiring.{u1} B _inst_8) _inst_4 _inst_9) {a : A}, (IsAlgebraic.{u2, u3} R A _inst_1 _inst_3 _inst_4 a) -> (IsAlgebraic.{u2, u1} R ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) a) _inst_1 _inst_8 _inst_9 (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (AlgHom.{u2, u3, u1} R A B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3) (Ring.toSemiring.{u1} B _inst_8) _inst_4 _inst_9) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u3 u1, u2, u3, u1} (AlgHom.{u2, u3, u1} R A B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3) (Ring.toSemiring.{u1} B _inst_8) _inst_4 _inst_9) R A B (SMulZeroClass.toSMul.{u2, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_3)))))) (DistribSMul.toSMulZeroClass.{u2, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_3)))))) (DistribMulAction.toDistribSMul.{u2, u3} R A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_3))))) (Module.toDistribMulAction.{u2, u3} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_3)))) (Algebra.toModule.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3) _inst_4))))) (SMulZeroClass.toSMul.{u2, u1} R B (AddMonoid.toZero.{u1} B (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B _inst_8)))))) (DistribSMul.toSMulZeroClass.{u2, u1} R B (AddMonoid.toAddZeroClass.{u1} B (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B _inst_8)))))) (DistribMulAction.toDistribSMul.{u2, u1} R B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B _inst_8))))) (Module.toDistribMulAction.{u2, u1} R B (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B _inst_8)))) (Algebra.toModule.{u2, u1} R B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} B _inst_8) _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u1, u2, u3, u1} (AlgHom.{u2, u3, u1} R A B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3) (Ring.toSemiring.{u1} B _inst_8) _inst_4 _inst_9) R A B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_3))))) (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B _inst_8))))) (Module.toDistribMulAction.{u2, u3} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_3)))) (Algebra.toModule.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3) _inst_4)) (Module.toDistribMulAction.{u2, u1} R B (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B _inst_8)))) (Algebra.toModule.{u2, u1} R B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} B _inst_8) _inst_9)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u1, u2, u3, u1} (AlgHom.{u2, u3, u1} R A B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3) (Ring.toSemiring.{u1} B _inst_8) _inst_4 _inst_9) R A B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B _inst_8))) (Module.toDistribMulAction.{u2, u3} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_3)))) (Algebra.toModule.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3) _inst_4)) (Module.toDistribMulAction.{u2, u1} R B (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B _inst_8)))) (Algebra.toModule.{u2, u1} R B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} B _inst_8) _inst_9)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u1, max u3 u1} R A B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3) (Ring.toSemiring.{u1} B _inst_8) _inst_4 _inst_9 (AlgHom.{u2, u3, u1} R A B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3) (Ring.toSemiring.{u1} B _inst_8) _inst_4 _inst_9) (AlgHom.algHomClass.{u2, u3, u1} R A B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3) (Ring.toSemiring.{u1} B _inst_8) _inst_4 _inst_9))))) f a))
 Case conversion may be inaccurate. Consider using '#align is_algebraic_alg_hom_of_is_algebraic isAlgebraic_algHom_of_isAlgebraicₓ'. -/
 /-- This is slightly more general than `is_algebraic_algebra_map_of_is_algebraic` in that it
   allows noncommutative intermediate rings `A`. -/
@@ -427,7 +427,7 @@ variable {K L}
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_6 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))], (Algebra.IsAlgebraic.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)) _inst_6) -> (forall (f : AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6), Function.Bijective.{succ u2, succ u2} L L (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) (fun (_x : AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) => L -> L) ([anonymous].{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) f))
 but is expected to have type
-  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_6 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))], (Algebra.IsAlgebraic.{u2, u1} K L (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) (DivisionRing.toRing.{u1} L (Field.toDivisionRing.{u1} L _inst_2)) _inst_6) -> (forall (f : AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6), Function.Bijective.{succ u1, succ u1} L L (FunLike.coe.{succ u1, succ u1, succ u1} (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : L) => L) _x) (SMulHomClass.toFunLike.{u1, u2, u1, u1} (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) K L L (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6))))) (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u2, u1, u1} (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) K L L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u2, u1, u1} (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) K L L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u1, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6 (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) (AlgHom.algHomClass.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6))))) f))
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_6 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))], (Algebra.IsAlgebraic.{u2, u1} K L (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) (DivisionRing.toRing.{u1} L (Field.toDivisionRing.{u1} L _inst_2)) _inst_6) -> (forall (f : AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6), Function.Bijective.{succ u1, succ u1} L L (FunLike.coe.{succ u1, succ u1, succ u1} (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : L) => L) _x) (SMulHomClass.toFunLike.{u1, u2, u1, u1} (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) K L L (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6))))) (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u2, u1, u1} (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) K L L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u2, u1, u1} (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) K L L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u1, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6 (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) (AlgHom.algHomClass.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6))))) f))
 Case conversion may be inaccurate. Consider using '#align algebra.is_algebraic.alg_hom_bijective Algebra.IsAlgebraic.algHom_bijectiveₓ'. -/
 theorem IsAlgebraic.algHom_bijective (ha : Algebra.IsAlgebraic K L) (f : L →ₐ[K] L) :
     Function.Bijective f :=
@@ -446,7 +446,7 @@ theorem IsAlgebraic.algHom_bijective (ha : Algebra.IsAlgebraic K L) (f : L →
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_6 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_14 : FiniteDimensional.{u1, u2} K L (Field.toDivisionRing.{u1} K _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6)] (ϕ : AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6), Function.Bijective.{succ u2, succ u2} L L (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) (fun (_x : AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) => L -> L) ([anonymous].{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) ϕ)
 but is expected to have type
-  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_6 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] [_inst_14 : FiniteDimensional.{u2, u1} K L (Field.toDivisionRing.{u2} K _inst_1) (Ring.toAddCommGroup.{u1} L (DivisionRing.toRing.{u1} L (Field.toDivisionRing.{u1} L _inst_2))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)] (ϕ : AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6), Function.Bijective.{succ u1, succ u1} L L (FunLike.coe.{succ u1, succ u1, succ u1} (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : L) => L) _x) (SMulHomClass.toFunLike.{u1, u2, u1, u1} (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) K L L (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6))))) (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u2, u1, u1} (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) K L L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u2, u1, u1} (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) K L L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u1, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6 (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) (AlgHom.algHomClass.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6))))) ϕ)
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_6 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] [_inst_14 : FiniteDimensional.{u2, u1} K L (Field.toDivisionRing.{u2} K _inst_1) (Ring.toAddCommGroup.{u1} L (DivisionRing.toRing.{u1} L (Field.toDivisionRing.{u1} L _inst_2))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)] (ϕ : AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6), Function.Bijective.{succ u1, succ u1} L L (FunLike.coe.{succ u1, succ u1, succ u1} (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : L) => L) _x) (SMulHomClass.toFunLike.{u1, u2, u1, u1} (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) K L L (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6))))) (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u2, u1, u1} (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) K L L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u2, u1, u1} (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) K L L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u1, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6 (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) (AlgHom.algHomClass.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6))))) ϕ)
 Case conversion may be inaccurate. Consider using '#align alg_hom.bijective AlgHom.bijectiveₓ'. -/
 theorem AlgHom.bijective [FiniteDimensional K L] (ϕ : L →ₐ[K] L) : Function.Bijective ϕ :=
   (Algebra.isAlgebraic_of_finite K L).algHom_bijective ϕ
@@ -545,7 +545,7 @@ variable {K L : Type _} [Field K] [Field L] [Algebra K L] (A : Subalgebra K L)
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_4 : Field.{u1} K] [_inst_5 : Field.{u2} L] [_inst_6 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5)))] {x : L} {p : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_4)))}, (Ne.{succ u2} L (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) _inst_6) (fun (_x : AlgHom.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) _inst_6) => (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) -> L) ([anonymous].{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) _inst_6) (Polynomial.aeval.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6 x) (Polynomial.divX.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) p)) (OfNat.ofNat.{u2} L 0 (OfNat.mk.{u2} L 0 (Zero.zero.{u2} L (MulZeroClass.toHasZero.{u2} L (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))))))))))) -> (Eq.{succ u2} L (Inv.inv.{u2} L (DivInvMonoid.toHasInv.{u2} L (DivisionRing.toDivInvMonoid.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) x) (HDiv.hDiv.{u2, u2, u2} L L L (instHDiv.{u2} L (DivInvMonoid.toHasDiv.{u2} L (DivisionRing.toDivInvMonoid.{u2} L (Field.toDivisionRing.{u2} L _inst_5)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) _inst_6) (fun (_x : AlgHom.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) _inst_6) => (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) -> L) ([anonymous].{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) _inst_6) (Polynomial.aeval.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6 x) (Polynomial.divX.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) p)) (HSub.hSub.{u2, u2, u2} L L L (instHSub.{u2} L (SubNegMonoid.toHasSub.{u2} L (AddGroup.toSubNegMonoid.{u2} L (AddGroupWithOne.toAddGroup.{u2} L (AddCommGroupWithOne.toAddGroupWithOne.{u2} L (Ring.toAddCommGroupWithOne.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5)))))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) _inst_6) (fun (_x : AlgHom.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) _inst_6) => (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) -> L) ([anonymous].{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) _inst_6) (Polynomial.aeval.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6 x) p) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))))) (fun (_x : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))))) => K -> L) (RingHom.hasCoeToFun.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))))) (algebraMap.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6) (Polynomial.coeff.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_4))) p (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))))))
 but is expected to have type
-  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_4 : Field.{u2} K] [_inst_5 : Field.{u1} L] [_inst_6 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))] {x : L} {p : Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))}, (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) (Polynomial.divX.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (fun (_x : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (SMulZeroClass.toSMul.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (AddMonoid.toZero.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))))) (DistribSMul.toSMulZeroClass.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))))) (DistribMulAction.toDistribSMul.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))))) (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) 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_inst_4)))) _inst_6 (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6))))) (Polynomial.aeval.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6 x) (Polynomial.divX.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p)) (HSub.hSub.{u1, u1, u1} ((fun 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=> L) p) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) p) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) p) _inst_5)))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K 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(Field.toSemifield.{u2} K _inst_4)))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K 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(AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) 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(Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6 (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6))))) (Polynomial.aeval.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6 x) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (RingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) K L (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (NonUnitalNonAssocSemiring.toMul.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))) (RingHom.instRingHomClassRingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (algebraMap.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6) (Polynomial.coeff.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_4 : Field.{u2} K] [_inst_5 : Field.{u1} L] [_inst_6 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))] {x : L} {p : Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))}, (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) (Polynomial.divX.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (fun (_x : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (SMulZeroClass.toSMul.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (AddMonoid.toZero.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))))) (DistribSMul.toSMulZeroClass.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))))) (DistribMulAction.toDistribSMul.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))))) (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6 (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6))))) (Polynomial.aeval.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6 x) (Polynomial.divX.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) (Polynomial.divX.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) (Polynomial.divX.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p)) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) 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K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 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(CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) 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_inst_4)))) _inst_6 (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K 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=> L) p) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) p) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) p) _inst_5)))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K 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(CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))))) (DistribMulAction.toDistribSMul.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))))) (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6 (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6))))) (Polynomial.aeval.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6 x) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (RingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) K L (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (NonUnitalNonAssocSemiring.toMul.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))) (RingHom.instRingHomClassRingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (algebraMap.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6) (Polynomial.coeff.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))
 Case conversion may be inaccurate. Consider using '#align inv_eq_of_aeval_div_X_ne_zero inv_eq_of_aeval_divX_ne_zeroₓ'. -/
 theorem inv_eq_of_aeval_divX_ne_zero {x : L} {p : K[X]} (aeval_ne : aeval x (divX p) ≠ 0) :
     x⁻¹ = aeval x (divX p) / (aeval x p - algebraMap _ _ (p.coeff 0)) :=
@@ -560,7 +560,7 @@ theorem inv_eq_of_aeval_divX_ne_zero {x : L} {p : K[X]} (aeval_ne : aeval x (div
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_4 : Field.{u1} K] [_inst_5 : Field.{u2} L] [_inst_6 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5)))] {x : L} {p : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_4)))}, (Eq.{succ u2} L (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) _inst_6) (fun (_x : AlgHom.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) _inst_6) => (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) -> L) ([anonymous].{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) _inst_6) (Polynomial.aeval.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6 x) p) (OfNat.ofNat.{u2} L 0 (OfNat.mk.{u2} L 0 (Zero.zero.{u2} L (MulZeroClass.toHasZero.{u2} L (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))))))))))) -> (Ne.{succ u1} K (Polynomial.coeff.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_4))) p (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_4))))))))))) -> (Eq.{succ u2} L (Inv.inv.{u2} L (DivInvMonoid.toHasInv.{u2} L (DivisionRing.toDivInvMonoid.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) x) (Neg.neg.{u2} L (SubNegMonoid.toHasNeg.{u2} L (AddGroup.toSubNegMonoid.{u2} L (AddGroupWithOne.toAddGroup.{u2} L (AddCommGroupWithOne.toAddGroupWithOne.{u2} L (Ring.toAddCommGroupWithOne.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))))))) (HDiv.hDiv.{u2, u2, u2} L L L (instHDiv.{u2} L (DivInvMonoid.toHasDiv.{u2} L (DivisionRing.toDivInvMonoid.{u2} L (Field.toDivisionRing.{u2} L _inst_5)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) _inst_6) (fun (_x : AlgHom.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) _inst_6) => (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) -> L) ([anonymous].{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) _inst_6) (Polynomial.aeval.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6 x) (Polynomial.divX.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) p)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))))) (fun (_x : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))))) => K -> L) (RingHom.hasCoeToFun.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))))) (algebraMap.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6) (Polynomial.coeff.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_4))) p (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))))))
 but is expected to have type
-  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_4 : Field.{u2} K] [_inst_5 : Field.{u1} L] [_inst_6 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))] {x : L} {p : Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (fun (_x : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (SMulZeroClass.toSMul.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (AddMonoid.toZero.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))))) (DistribSMul.toSMulZeroClass.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))))) (DistribMulAction.toDistribSMul.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))))) (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K 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(Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6 (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6))))) (Polynomial.aeval.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6 x) (Polynomial.divX.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (RingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) K L (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (NonUnitalNonAssocSemiring.toMul.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))) (RingHom.instRingHomClassRingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (algebraMap.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6) (Polynomial.coeff.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_4 : Field.{u2} K] [_inst_5 : Field.{u1} L] [_inst_6 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))] {x : L} {p : Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (fun (_x : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (SMulZeroClass.toSMul.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (AddMonoid.toZero.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))))) (DistribSMul.toSMulZeroClass.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))))) (DistribMulAction.toDistribSMul.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))))) (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K 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_inst_5))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K 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(Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6))))) (Polynomial.aeval.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6 x) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))))) (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6 (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6))))) (Polynomial.aeval.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6 x) (Polynomial.divX.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (RingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) K L (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (NonUnitalNonAssocSemiring.toMul.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))) (RingHom.instRingHomClassRingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (algebraMap.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6) (Polynomial.coeff.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))
 Case conversion may be inaccurate. Consider using '#align inv_eq_of_root_of_coeff_zero_ne_zero inv_eq_of_root_of_coeff_zero_ne_zeroₓ'. -/
 theorem inv_eq_of_root_of_coeff_zero_ne_zero {x : L} {p : K[X]} (aeval_eq : aeval x p = 0)
     (coeff_zero_ne : p.coeff 0 ≠ 0) : x⁻¹ = -(aeval x (divX p) / algebraMap _ _ (p.coeff 0)) :=
@@ -577,7 +577,7 @@ theorem inv_eq_of_root_of_coeff_zero_ne_zero {x : L} {p : K[X]} (aeval_eq : aeva
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_4 : Field.{u1} K] [_inst_5 : Field.{u2} L] [_inst_6 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5)))] (A : Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6) {x : coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6)) A} {p : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_4)))}, (Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6)) A) (coeFn.{max (succ 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(Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6) L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5)))) (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6) (Subalgebra.subsemiringClass.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6))) A))))) -> (Ne.{succ u1} K (Polynomial.coeff.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_4))) p (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K 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(DivisionRing.toDivInvMonoid.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6)) A) L (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K 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(coeSubtype.{succ u2} L (fun (x : L) => Membership.Mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6)) x A))))) x)) A)
 but is expected to have type
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(Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)} {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))}, (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) => Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) p) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgHom.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K 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(Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)) K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (SMulZeroClass.toSMul.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))))))) (DistribMulAction.toDistribSMul.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))))))) (Module.toDistribMulAction.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))))) (Algebra.toModule.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))))))) (SMulZeroClass.toSMul.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (AddMonoid.toZero.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)))))) (DistribSMul.toSMulZeroClass.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)))))) (DistribMulAction.toDistribSMul.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K 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(DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)))) (Algebra.toModule.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)) K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A))))) (Module.toDistribMulAction.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))))) (Algebra.toModule.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)))) (Algebra.toModule.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)) K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A))) (Module.toDistribMulAction.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))))) (Algebra.toModule.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)))) (Algebra.toModule.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (AlgHom.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L 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(DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)) (AlgHom.algHomClass.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L 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(Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)))))) (Polynomial.aeval.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L 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K (Field.toSemifield.{u1} K _inst_4)))) => Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) p) (ZeroMemClass.zero.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (CommMonoidWithZero.toZero.{u2} L (CommGroupWithZero.toCommMonoidWithZero.{u2} L (Semifield.toCommGroupWithZero.{u2} L (Field.toSemifield.{u2} L _inst_5)))) (AddSubmonoidClass.toZeroMemClass.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (AddMonoid.toAddZeroClass.{u2} L (AddMonoidWithOne.toAddMonoid.{u2} L (AddGroupWithOne.toAddMonoidWithOne.{u2} L (Ring.toAddGroupWithOne.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5)))))) (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SubsemiringClass.toAddSubmonoidClass.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5)))) (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (Subalgebra.SubsemiringClass.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6))) A)))) -> (Ne.{succ u1} K (Polynomial.coeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) p (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_4))))))) -> (Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) (Inv.inv.{u2} L (Field.toInv.{u2} L _inst_5) (Subtype.val.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Set.{u2} L) (Set.instMembershipSet.{u2} L) x (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) A)) x)) A)
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_4 : Field.{u1} K] [_inst_5 : Field.{u2} L] [_inst_6 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5)))] (A : Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) {x : Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)} {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))}, (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) => Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) p) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgHom.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)) (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (fun (_x : Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) => Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)) K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (SMulZeroClass.toSMul.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))))))) (DistribMulAction.toDistribSMul.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))))))) (Module.toDistribMulAction.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))))) (Algebra.toModule.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))))))) (SMulZeroClass.toSMul.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (AddMonoid.toZero.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)))))) (DistribSMul.toSMulZeroClass.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)))))) (DistribMulAction.toDistribSMul.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)))) (Algebra.toModule.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)) K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A))))) (Module.toDistribMulAction.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))))) (Algebra.toModule.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)))) (Algebra.toModule.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)) K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A))) (Module.toDistribMulAction.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))))) (Algebra.toModule.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)))) (Algebra.toModule.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (AlgHom.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)) (AlgHom.algHomClass.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)))))) (Polynomial.aeval.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) x) p) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) => Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) p) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) => Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) p) (ZeroMemClass.zero.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (CommMonoidWithZero.toZero.{u2} L (CommGroupWithZero.toCommMonoidWithZero.{u2} L (Semifield.toCommGroupWithZero.{u2} L (Field.toSemifield.{u2} L _inst_5)))) (AddSubmonoidClass.toZeroMemClass.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (AddMonoid.toAddZeroClass.{u2} L (AddMonoidWithOne.toAddMonoid.{u2} L (AddGroupWithOne.toAddMonoidWithOne.{u2} L (Ring.toAddGroupWithOne.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5)))))) (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SubsemiringClass.toAddSubmonoidClass.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5)))) (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (Subalgebra.SubsemiringClass.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6))) A)))) -> (Ne.{succ u1} K (Polynomial.coeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) p (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_4))))))) -> (Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) (Inv.inv.{u2} L (Field.toInv.{u2} L _inst_5) (Subtype.val.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Set.{u2} L) (Set.instMembershipSet.{u2} L) x (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) A)) x)) A)
 Case conversion may be inaccurate. Consider using '#align subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zeroₓ'. -/
 theorem Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero {x : A} {p : K[X]}
     (aeval_eq : aeval x p = 0) (coeff_zero_ne : p.coeff 0 ≠ 0) : (x⁻¹ : L) ∈ A :=
@@ -703,7 +703,7 @@ attribute [local instance] Polynomial.algebraPi
 lean 3 declaration is
   forall (R' : Type.{u1}) (S' : Type.{u2}) (T' : Type.{u3}) [_inst_4 : CommSemiring.{u1} R'] [_inst_5 : CommSemiring.{u2} S'] [_inst_6 : CommSemiring.{u3} T'] [_inst_7 : Algebra.{u1, u2} R' S' _inst_4 (CommSemiring.toSemiring.{u2} S' _inst_5)] [_inst_8 : Algebra.{u2, u3} S' T' _inst_5 (CommSemiring.toSemiring.{u3} T' _inst_6)], Eq.{max (succ u1) (succ u2) (succ u3)} ((fun (_x : RingHom.{u1, max u2 u3} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (S' -> T') (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.commSemiring.{u1} R' _inst_4))) (Semiring.toNonAssocSemiring.{max u2 u3} (S' -> T') (Pi.semiring.{u2, u3} S' (fun (ᾰ : S') => T') (fun (i : S') => CommSemiring.toSemiring.{u3} T' _inst_6)))) => (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) -> S' -> T') (algebraMap.{u1, max u2 u3} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (S' -> T') (Polynomial.commSemiring.{u1} R' _inst_4) (Pi.semiring.{u2, u3} S' (fun (ᾰ : S') => T') (fun (i : S') => CommSemiring.toSemiring.{u3} T' _inst_6)) (Polynomial.algebraPi.{u1, u2, u3} R' S' T' _inst_4 _inst_5 _inst_6 _inst_7 _inst_8))) (coeFn.{max (succ u1) (succ (max u2 u3)), max (succ u1) (succ (max u2 u3))} (RingHom.{u1, max u2 u3} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (S' -> T') (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.commSemiring.{u1} R' _inst_4))) (Semiring.toNonAssocSemiring.{max u2 u3} (S' -> T') (Pi.semiring.{u2, u3} S' (fun (ᾰ : S') => T') (fun (i : S') => CommSemiring.toSemiring.{u3} T' _inst_6)))) (fun (_x : RingHom.{u1, max u2 u3} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (S' -> T') (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.commSemiring.{u1} R' _inst_4))) (Semiring.toNonAssocSemiring.{max u2 u3} (S' -> T') (Pi.semiring.{u2, u3} S' (fun (ᾰ : S') => T') (fun (i : S') => CommSemiring.toSemiring.{u3} T' _inst_6)))) => (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) -> S' -> T') (RingHom.hasCoeToFun.{u1, max u2 u3} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (S' -> T') (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.commSemiring.{u1} R' _inst_4))) (Semiring.toNonAssocSemiring.{max u2 u3} (S' -> T') (Pi.semiring.{u2, u3} S' (fun (ᾰ : S') => T') (fun (i : S') => CommSemiring.toSemiring.{u3} T' _inst_6)))) (algebraMap.{u1, max u2 u3} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (S' -> T') (Polynomial.commSemiring.{u1} R' _inst_4) (Pi.semiring.{u2, u3} S' (fun (ᾰ : S') => T') (fun (i : S') => CommSemiring.toSemiring.{u3} T' _inst_6)) (Polynomial.algebraPi.{u1, u2, u3} R' S' T' _inst_4 _inst_5 _inst_6 _inst_7 _inst_8))) (fun (p : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (z : S') => coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} S' T' (Semiring.toNonAssocSemiring.{u2} S' (CommSemiring.toSemiring.{u2} S' _inst_5)) (Semiring.toNonAssocSemiring.{u3} T' (CommSemiring.toSemiring.{u3} T' _inst_6))) (fun (_x : RingHom.{u2, u3} S' T' (Semiring.toNonAssocSemiring.{u2} S' (CommSemiring.toSemiring.{u2} S' _inst_5)) (Semiring.toNonAssocSemiring.{u3} T' (CommSemiring.toSemiring.{u3} T' _inst_6))) => S' -> T') (RingHom.hasCoeToFun.{u2, u3} S' T' (Semiring.toNonAssocSemiring.{u2} S' (CommSemiring.toSemiring.{u2} S' _inst_5)) (Semiring.toNonAssocSemiring.{u3} T' (CommSemiring.toSemiring.{u3} T' _inst_6))) (algebraMap.{u2, u3} S' T' _inst_5 (CommSemiring.toSemiring.{u3} T' _inst_6) _inst_8) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) S' _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u2} S' _inst_5) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)) _inst_7) (fun (_x : AlgHom.{u1, u1, u2} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) S' _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u2} S' _inst_5) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)) _inst_7) => (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) -> S') ([anonymous].{u1, u1, u2} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) S' _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u2} S' _inst_5) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)) _inst_7) (Polynomial.aeval.{u1, u2} R' S' _inst_4 (CommSemiring.toSemiring.{u2} S' _inst_5) _inst_7 z) p))
 but is expected to have type
-  forall (R' : Type.{u1}) (S' : Type.{u2}) (T' : Type.{u3}) [_inst_4 : CommSemiring.{u1} R'] [_inst_5 : CommSemiring.{u2} S'] [_inst_6 : CommSemiring.{u3} T'] [_inst_7 : Algebra.{u1, u2} R' S' _inst_4 (CommSemiring.toSemiring.{u2} S' _inst_5)] [_inst_8 : Algebra.{u2, u3} S' T' _inst_5 (CommSemiring.toSemiring.{u3} T' _inst_6)], Eq.{max (max (succ u1) (succ u2)) (succ u3)} (forall (a : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S' -> T') a) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u1, max (succ u2) (succ u3)} (RingHom.{u1, max u2 u3} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (S' -> T') (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.commSemiring.{u1} R' _inst_4))) (Semiring.toNonAssocSemiring.{max u2 u3} (S' -> T') (Pi.semiring.{u2, u3} S' (fun (a._@.Mathlib.RingTheory.Algebraic._hyg.5653 : S') => T') (fun (i : S') => CommSemiring.toSemiring.{u3} T' _inst_6)))) (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (fun (_x : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S' -> T') _x) (MulHomClass.toFunLike.{max (max u1 u2) u3, u1, max u2 u3} (RingHom.{u1, max u2 u3} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (S' -> T') (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.commSemiring.{u1} R' _inst_4))) (Semiring.toNonAssocSemiring.{max u2 u3} (S' -> T') (Pi.semiring.{u2, u3} S' (fun (a._@.Mathlib.RingTheory.Algebraic._hyg.5653 : S') => T') (fun (i : S') => CommSemiring.toSemiring.{u3} T' _inst_6)))) (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (S' -> T') (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.commSemiring.{u1} R' _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{max u2 u3} (S' -> T') (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (S' -> T') (Semiring.toNonAssocSemiring.{max u2 u3} (S' -> T') (Pi.semiring.{u2, u3} S' (fun (a._@.Mathlib.RingTheory.Algebraic._hyg.5653 : S') => T') (fun (i : S') => CommSemiring.toSemiring.{u3} T' _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u2) u3, u1, max u2 u3} (RingHom.{u1, max u2 u3} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (S' -> T') (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.commSemiring.{u1} R' _inst_4))) (Semiring.toNonAssocSemiring.{max u2 u3} (S' -> T') (Pi.semiring.{u2, u3} S' (fun (a._@.Mathlib.RingTheory.Algebraic._hyg.5653 : S') => T') (fun (i : S') => CommSemiring.toSemiring.{u3} T' _inst_6)))) (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (S' -> T') (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.commSemiring.{u1} R' _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (S' -> T') (Semiring.toNonAssocSemiring.{max u2 u3} (S' -> T') (Pi.semiring.{u2, u3} S' (fun (a._@.Mathlib.RingTheory.Algebraic._hyg.5653 : S') => T') (fun (i : S') => CommSemiring.toSemiring.{u3} T' _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u1 u2) u3, u1, max u2 u3} (RingHom.{u1, max u2 u3} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (S' -> T') (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.commSemiring.{u1} R' _inst_4))) (Semiring.toNonAssocSemiring.{max u2 u3} (S' -> T') (Pi.semiring.{u2, u3} S' (fun (a._@.Mathlib.RingTheory.Algebraic._hyg.5653 : S') => T') (fun (i : S') => CommSemiring.toSemiring.{u3} T' _inst_6)))) (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (S' -> T') (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.commSemiring.{u1} R' _inst_4))) (Semiring.toNonAssocSemiring.{max u2 u3} (S' -> T') (Pi.semiring.{u2, u3} S' (fun (a._@.Mathlib.RingTheory.Algebraic._hyg.5653 : S') => T') (fun (i : S') => CommSemiring.toSemiring.{u3} T' _inst_6))) (RingHom.instRingHomClassRingHom.{u1, max u2 u3} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (S' -> T') (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.commSemiring.{u1} R' _inst_4))) (Semiring.toNonAssocSemiring.{max u2 u3} (S' -> T') (Pi.semiring.{u2, u3} S' (fun (a._@.Mathlib.RingTheory.Algebraic._hyg.5653 : S') => T') (fun (i : S') => CommSemiring.toSemiring.{u3} T' _inst_6))))))) (algebraMap.{u1, max u2 u3} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (S' -> T') (Polynomial.commSemiring.{u1} R' _inst_4) (Pi.semiring.{u2, u3} S' (fun (ᾰ : S') => T') (fun (i : S') => CommSemiring.toSemiring.{u3} T' _inst_6)) (Polynomial.algebraPi.{u1, u2, u3} R' S' T' _inst_4 _inst_5 _inst_6 _inst_7 _inst_8))) (fun (p : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (z : S') => FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (RingHom.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) T' (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) _inst_5)) (Semiring.toNonAssocSemiring.{u3} T' (CommSemiring.toSemiring.{u3} T' _inst_6))) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) => T') _x) (MulHomClass.toFunLike.{max u3 u2, u2, u3} (RingHom.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) T' (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) _inst_5)) (Semiring.toNonAssocSemiring.{u3} T' (CommSemiring.toSemiring.{u3} T' _inst_6))) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) T' (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) _inst_5)))) (NonUnitalNonAssocSemiring.toMul.{u3} T' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T' (Semiring.toNonAssocSemiring.{u3} T' (CommSemiring.toSemiring.{u3} T' _inst_6)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u2, u3} (RingHom.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) T' (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) _inst_5)) (Semiring.toNonAssocSemiring.{u3} T' (CommSemiring.toSemiring.{u3} T' _inst_6))) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) T' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) _inst_5))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} T' (Semiring.toNonAssocSemiring.{u3} T' (CommSemiring.toSemiring.{u3} T' _inst_6))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u2, u3} (RingHom.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) T' (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) _inst_5)) (Semiring.toNonAssocSemiring.{u3} T' (CommSemiring.toSemiring.{u3} T' _inst_6))) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) T' (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) _inst_5)) (Semiring.toNonAssocSemiring.{u3} T' (CommSemiring.toSemiring.{u3} T' _inst_6)) (RingHom.instRingHomClassRingHom.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) T' (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) _inst_5)) (Semiring.toNonAssocSemiring.{u3} T' (CommSemiring.toSemiring.{u3} T' _inst_6)))))) (algebraMap.{u2, u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S') p) T' _inst_5 (CommSemiring.toSemiring.{u3} T' _inst_6) _inst_8) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgHom.{u1, u1, u2} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) S' _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u2} S' _inst_5) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)) _inst_7) (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (fun (_x : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => (fun 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4))))))) (DistribMulAction.toDistribSMul.{u1, u1} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)))))) (Module.toDistribMulAction.{u1, u1} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} R' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4))))) (Algebra.toModule.{u1, u1} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4))))))) (SMulZeroClass.toSMul.{u1, u2} R' S' (AddMonoid.toZero.{u2} S' (AddCommMonoid.toAddMonoid.{u2} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S' (Semiring.toNonAssocSemiring.{u2} S' (CommSemiring.toSemiring.{u2} S' _inst_5)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R' S' (AddMonoid.toAddZeroClass.{u2} S' (AddCommMonoid.toAddMonoid.{u2} S' 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u2} (AlgHom.{u1, u1, u2} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) S' _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u2} S' _inst_5) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)) _inst_7) R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) S' (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)))))) (AddCommMonoid.toAddMonoid.{u2} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S' (Semiring.toNonAssocSemiring.{u2} S' (CommSemiring.toSemiring.{u2} S' _inst_5))))) (Module.toDistribMulAction.{u1, u1} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} R' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4))))) (Algebra.toModule.{u1, u1} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)))) (Module.toDistribMulAction.{u1, u2} R' S' (CommSemiring.toSemiring.{u1} R' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S' (Semiring.toNonAssocSemiring.{u2} S' (CommSemiring.toSemiring.{u2} S' _inst_5)))) (Algebra.toModule.{u1, u2} R' S' _inst_4 (CommSemiring.toSemiring.{u2} S' _inst_5) _inst_7)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) S' _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u2} S' _inst_5) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)) _inst_7) R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) S' (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S' (Semiring.toNonAssocSemiring.{u2} S' (CommSemiring.toSemiring.{u2} S' _inst_5))) (Module.toDistribMulAction.{u1, u1} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} R' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4))))) (Algebra.toModule.{u1, u1} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)))) (Module.toDistribMulAction.{u1, u2} R' S' (CommSemiring.toSemiring.{u1} R' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S' (Semiring.toNonAssocSemiring.{u2} S' (CommSemiring.toSemiring.{u2} S' _inst_5)))) (Algebra.toModule.{u1, u2} R' S' _inst_4 (CommSemiring.toSemiring.{u2} S' _inst_5) _inst_7)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) S' _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u2} S' _inst_5) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)) _inst_7 (AlgHom.{u1, u1, u2} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) S' _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u2} S' _inst_5) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)) _inst_7) (AlgHom.algHomClass.{u1, u1, u2} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) S' _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u2} S' _inst_5) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)) _inst_7))))) (Polynomial.aeval.{u1, u2} R' S' _inst_4 (CommSemiring.toSemiring.{u2} S' _inst_5) _inst_7 z) p))
+  forall (R' : Type.{u1}) (S' : Type.{u2}) (T' : Type.{u3}) [_inst_4 : CommSemiring.{u1} R'] [_inst_5 : CommSemiring.{u2} S'] [_inst_6 : CommSemiring.{u3} T'] [_inst_7 : Algebra.{u1, u2} R' S' _inst_4 (CommSemiring.toSemiring.{u2} S' _inst_5)] [_inst_8 : Algebra.{u2, u3} S' T' _inst_5 (CommSemiring.toSemiring.{u3} T' _inst_6)], Eq.{max (max (succ u1) (succ u2)) (succ u3)} (forall (a : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => S' -> T') a) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u1, max (succ u2) (succ u3)} (RingHom.{u1, max u2 u3} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (S' -> T') (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.commSemiring.{u1} R' _inst_4))) 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(DistribMulAction.toDistribSMul.{u1, u1} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)))))) (Module.toDistribMulAction.{u1, u1} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} R' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4))))) (Algebra.toModule.{u1, u1} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4))))))) (SMulZeroClass.toSMul.{u1, u2} R' S' (AddMonoid.toZero.{u2} S' (AddCommMonoid.toAddMonoid.{u2} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S' (Semiring.toNonAssocSemiring.{u2} S' (CommSemiring.toSemiring.{u2} S' _inst_5)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R' S' (AddMonoid.toAddZeroClass.{u2} S' (AddCommMonoid.toAddMonoid.{u2} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S' (Semiring.toNonAssocSemiring.{u2} S' (CommSemiring.toSemiring.{u2} S' _inst_5)))))) (DistribMulAction.toDistribSMul.{u1, u2} R' S' (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4))) (AddCommMonoid.toAddMonoid.{u2} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S' (Semiring.toNonAssocSemiring.{u2} S' (CommSemiring.toSemiring.{u2} S' _inst_5))))) (Module.toDistribMulAction.{u1, u2} R' S' (CommSemiring.toSemiring.{u1} R' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S' (Semiring.toNonAssocSemiring.{u2} S' (CommSemiring.toSemiring.{u2} S' _inst_5)))) (Algebra.toModule.{u1, u2} R' S' _inst_4 (CommSemiring.toSemiring.{u2} S' _inst_5) _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) S' _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u2} S' _inst_5) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)) _inst_7) R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) S' (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)))))) (AddCommMonoid.toAddMonoid.{u2} S' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S' (Semiring.toNonAssocSemiring.{u2} S' (CommSemiring.toSemiring.{u2} S' _inst_5))))) (Module.toDistribMulAction.{u1, u1} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} R' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4))))) (Algebra.toModule.{u1, u1} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)))) (Module.toDistribMulAction.{u1, u2} R' S' (CommSemiring.toSemiring.{u1} R' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S' (Semiring.toNonAssocSemiring.{u2} S' (CommSemiring.toSemiring.{u2} S' _inst_5)))) (Algebra.toModule.{u1, u2} R' S' _inst_4 (CommSemiring.toSemiring.{u2} S' _inst_5) _inst_7)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) S' _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u2} S' _inst_5) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)) _inst_7) R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) S' (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S' (Semiring.toNonAssocSemiring.{u2} S' (CommSemiring.toSemiring.{u2} S' _inst_5))) (Module.toDistribMulAction.{u1, u1} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} R' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4))))) (Algebra.toModule.{u1, u1} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)))) (Module.toDistribMulAction.{u1, u2} R' S' (CommSemiring.toSemiring.{u1} R' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S' (Semiring.toNonAssocSemiring.{u2} S' (CommSemiring.toSemiring.{u2} S' _inst_5)))) (Algebra.toModule.{u1, u2} R' S' _inst_4 (CommSemiring.toSemiring.{u2} S' _inst_5) _inst_7)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) S' _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u2} S' _inst_5) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)) _inst_7 (AlgHom.{u1, u1, u2} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) S' _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u2} S' _inst_5) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)) _inst_7) (AlgHom.algHomClass.{u1, u1, u2} R' (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) S' _inst_4 (Polynomial.semiring.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u2} S' _inst_5) (Polynomial.algebraOfAlgebra.{u1, u1} R' R' _inst_4 (CommSemiring.toSemiring.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)) _inst_7))))) (Polynomial.aeval.{u1, u2} R' S' _inst_4 (CommSemiring.toSemiring.{u2} S' _inst_5) _inst_7 z) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.algebra_map_pi_eq_aeval Polynomial.algebraMap_pi_eq_aevalₓ'. -/
 @[simp]
 theorem Polynomial.algebraMap_pi_eq_aeval :

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 
 ! This file was ported from Lean 3 source module ring_theory.algebraic
-! leanprover-community/mathlib commit 2196ab363eb097c008d4497125e0dde23fb36db2
+! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Data.Polynomial.IntegralNormalization
 /-!
 # Algebraic elements and algebraic extensions
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 An element of an R-algebra is algebraic over R if it is the root of a nonzero polynomial.
 An R-algebra is algebraic over R if and only if all its elements are algebraic over R.
 The main result in this file proves transitivity of algebraicity:

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

@@ -32,37 +32,53 @@ section
 
 variable (R : Type u) {A : Type v} [CommRing R] [Ring A] [Algebra R A]
 
+#print IsAlgebraic /-
 /-- An element of an R-algebra is algebraic over R if it is a root of a nonzero polynomial
 with coefficients in R. -/
 def IsAlgebraic (x : A) : Prop :=
   ∃ p : R[X], p ≠ 0 ∧ aeval x p = 0
 #align is_algebraic IsAlgebraic
+-/
 
+#print Transcendental /-
 /-- An element of an R-algebra is transcendental over R if it is not algebraic over R. -/
 def Transcendental (x : A) : Prop :=
   ¬IsAlgebraic R x
 #align transcendental Transcendental
+-/
 
+#print is_transcendental_of_subsingleton /-
 theorem is_transcendental_of_subsingleton [Subsingleton R] (x : A) : Transcendental R x :=
   fun ⟨p, h, _⟩ => h <| Subsingleton.elim p 0
 #align is_transcendental_of_subsingleton is_transcendental_of_subsingleton
+-/
 
 variable {R}
 
+#print Subalgebra.IsAlgebraic /-
 /-- A subalgebra is algebraic if all its elements are algebraic. -/
 def Subalgebra.IsAlgebraic (S : Subalgebra R A) : Prop :=
   ∀ x ∈ S, IsAlgebraic R x
 #align subalgebra.is_algebraic Subalgebra.IsAlgebraic
+-/
 
 variable (R A)
 
+#print Algebra.IsAlgebraic /-
 /-- An algebra is algebraic if all its elements are algebraic. -/
 def Algebra.IsAlgebraic : Prop :=
   ∀ x : A, IsAlgebraic R x
 #align algebra.is_algebraic Algebra.IsAlgebraic
+-/
 
 variable {R A}
 
+/- warning: subalgebra.is_algebraic_iff -> Subalgebra.isAlgebraic_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Ring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2)] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3), Iff (Subalgebra.IsAlgebraic.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Algebra.IsAlgebraic.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3)) S) _inst_1 (Subalgebra.toRing.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3 S))
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Ring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2)] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3), Iff (Subalgebra.IsAlgebraic.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Algebra.IsAlgebraic.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3)) x S)) _inst_1 (Subalgebra.toRing.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3 S))
+Case conversion may be inaccurate. Consider using '#align subalgebra.is_algebraic_iff Subalgebra.isAlgebraic_iffₓ'. -/
 /-- A subalgebra is algebraic if and only if it is algebraic as an algebra. -/
 theorem Subalgebra.isAlgebraic_iff (S : Subalgebra R A) :
     S.IsAlgebraic ↔ @Algebra.IsAlgebraic R S _ _ S.Algebra :=
@@ -75,6 +91,12 @@ theorem Subalgebra.isAlgebraic_iff (S : Subalgebra R A) :
   rw [← aeval_alg_hom_apply, S.val_apply]
 #align subalgebra.is_algebraic_iff Subalgebra.isAlgebraic_iff
 
+/- warning: algebra.is_algebraic_iff -> Algebra.isAlgebraic_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Ring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2)], Iff (Algebra.IsAlgebraic.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Subalgebra.IsAlgebraic.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Top.top.{u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) (CompleteLattice.toHasTop.{u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3))))
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Ring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2)], Iff (Algebra.IsAlgebraic.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Subalgebra.IsAlgebraic.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Top.top.{u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_2) _inst_3))))
+Case conversion may be inaccurate. Consider using '#align algebra.is_algebraic_iff Algebra.isAlgebraic_iffₓ'. -/
 /-- An algebra is algebraic if and only if it is algebraic as a subalgebra. -/
 theorem Algebra.isAlgebraic_iff : Algebra.IsAlgebraic R A ↔ (⊤ : Subalgebra R A).IsAlgebraic :=
   by
@@ -82,10 +104,12 @@ theorem Algebra.isAlgebraic_iff : Algebra.IsAlgebraic R A ↔ (⊤ : Subalgebra
   simp only [Algebra.mem_top, forall_prop_of_true, iff_self_iff]
 #align algebra.is_algebraic_iff Algebra.isAlgebraic_iff
 
+#print isAlgebraic_iff_not_injective /-
 theorem isAlgebraic_iff_not_injective {x : A} :
     IsAlgebraic R x ↔ ¬Function.Injective (Polynomial.aeval x : R[X] →ₐ[R] A) := by
   simp only [IsAlgebraic, injective_iff_map_eq_zero, not_forall, and_comm, exists_prop]
 #align is_algebraic_iff_not_injective isAlgebraic_iff_not_injective
+-/
 
 end
 
@@ -97,58 +121,110 @@ variable [CommRing S] [Ring A] [Algebra R A] [Algebra R S] [Algebra S A]
 
 variable [IsScalarTower R S A]
 
+#print IsIntegral.isAlgebraic /-
 /-- An integral element of an algebra is algebraic.-/
 theorem IsIntegral.isAlgebraic [Nontrivial R] {x : A} : IsIntegral R x → IsAlgebraic R x :=
   fun ⟨p, hp, hpx⟩ => ⟨p, hp.NeZero, hpx⟩
 #align is_integral.is_algebraic IsIntegral.isAlgebraic
+-/
 
 variable {R}
 
+/- warning: is_algebraic_zero -> isAlgebraic_zero is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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 theorem isAlgebraic_zero [Nontrivial R] : IsAlgebraic R (0 : A) :=
   ⟨_, X_ne_zero, aeval_X 0⟩
 #align is_algebraic_zero isAlgebraic_zero
 
+/- warning: is_algebraic_algebra_map -> isAlgebraic_algebraMap is a dubious translation:
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 /-- An element of `R` is algebraic, when viewed as an element of the `R`-algebra `A`. -/
 theorem isAlgebraic_algebraMap [Nontrivial R] (x : R) : IsAlgebraic R (algebraMap R A x) :=
   ⟨_, X_sub_C_ne_zero x, by rw [_root_.map_sub, aeval_X, aeval_C, sub_self]⟩
 #align is_algebraic_algebra_map isAlgebraic_algebraMap
 
+/- warning: is_algebraic_one -> isAlgebraic_one is a dubious translation:
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 theorem isAlgebraic_one [Nontrivial R] : IsAlgebraic R (1 : A) :=
   by
   rw [← _root_.map_one _]
   exact isAlgebraic_algebraMap 1
 #align is_algebraic_one isAlgebraic_one
 
+/- warning: is_algebraic_nat -> isAlgebraic_nat is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align is_algebraic_nat isAlgebraic_natₓ'. -/
 theorem isAlgebraic_nat [Nontrivial R] (n : ℕ) : IsAlgebraic R (n : A) :=
   by
   rw [← map_natCast _]
   exact isAlgebraic_algebraMap n
 #align is_algebraic_nat isAlgebraic_nat
 
+/- warning: is_algebraic_int -> isAlgebraic_int is a dubious translation:
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 theorem isAlgebraic_int [Nontrivial R] (n : ℤ) : IsAlgebraic R (n : A) :=
   by
   rw [← _root_.map_int_cast (algebraMap R A)]
   exact isAlgebraic_algebraMap n
 #align is_algebraic_int isAlgebraic_int
 
+/- warning: is_algebraic_rat -> isAlgebraic_rat is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align is_algebraic_rat isAlgebraic_ratₓ'. -/
 theorem isAlgebraic_rat (R : Type u) {A : Type v} [DivisionRing A] [Field R] [Algebra R A] (n : ℚ) :
     IsAlgebraic R (n : A) := by
   rw [← map_ratCast (algebraMap R A)]
   exact isAlgebraic_algebraMap n
 #align is_algebraic_rat isAlgebraic_rat
 
+#print isAlgebraic_of_mem_rootSet /-
 theorem isAlgebraic_of_mem_rootSet {R : Type u} {A : Type v} [Field R] [Field A] [Algebra R A]
     {p : R[X]} {x : A} (hx : x ∈ p.rootSet A) : IsAlgebraic R x :=
   ⟨p, ne_zero_of_mem_rootSet hx, aeval_eq_zero_of_mem_rootSet hx⟩
 #align is_algebraic_of_mem_root_set isAlgebraic_of_mem_rootSet
+-/
 
 open IsScalarTower
 
+/- warning: is_algebraic_algebra_map_of_is_algebraic -> isAlgebraic_algebraMap_of_isAlgebraic is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u3}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u3} S] [_inst_3 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u3} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))] [_inst_6 : Algebra.{u3, u2} S A (CommRing.toCommSemiring.{u3} S _inst_2) (Ring.toSemiring.{u2} A _inst_3)] [_inst_7 : IsScalarTower.{u1, u3, u2} R S A (SMulZeroClass.toHasSmul.{u1, u3} R S (AddZeroClass.toHasZero.{u3} S (AddMonoid.toAddZeroClass.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} S (AddMonoid.toAddZeroClass.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} S (AddMonoid.toAddZeroClass.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u3} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))))) (Algebra.toModule.{u1, u3} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u2} S A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_3))))))) (SMulWithZero.toSmulZeroClass.{u3, u2} S A (MulZeroClass.toHasZero.{u3} S (MulZeroOneClass.toMulZeroClass.{u3} S (MonoidWithZero.toMulZeroOneClass.{u3} S (Semiring.toMonoidWithZero.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_3))))))) (MulActionWithZero.toSMulWithZero.{u3, u2} S A (Semiring.toMonoidWithZero.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_3))))))) (Module.toMulActionWithZero.{u3, u2} S A (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_3)))) (Algebra.toModule.{u3, u2} S A 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(Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_3))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_3)))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3) _inst_4)))))] {a : S}, (IsAlgebraic.{u1, u3} R S _inst_1 (CommRing.toRing.{u3} S _inst_2) _inst_5 a) -> (IsAlgebraic.{u1, u2} R A _inst_1 _inst_3 _inst_4 (coeFn.{max (succ u3) (succ u2), max (succ u3) (succ u2)} 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+Case conversion may be inaccurate. Consider using '#align is_algebraic_algebra_map_of_is_algebraic isAlgebraic_algebraMap_of_isAlgebraicₓ'. -/
 theorem isAlgebraic_algebraMap_of_isAlgebraic {a : S} :
     IsAlgebraic R a → IsAlgebraic R (algebraMap S A a) := fun ⟨f, hf₁, hf₂⟩ =>
   ⟨f, hf₁, by rw [aeval_algebra_map_apply, hf₂, map_zero]⟩
 #align is_algebraic_algebra_map_of_is_algebraic isAlgebraic_algebraMap_of_isAlgebraic
 
+/- warning: is_algebraic_alg_hom_of_is_algebraic -> isAlgebraic_algHom_of_isAlgebraic is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align is_algebraic_alg_hom_of_is_algebraic isAlgebraic_algHom_of_isAlgebraicₓ'. -/
 /-- This is slightly more general than `is_algebraic_algebra_map_of_is_algebraic` in that it
   allows noncommutative intermediate rings `A`. -/
 theorem isAlgebraic_algHom_of_isAlgebraic {B} [Ring B] [Algebra R B] (f : A →ₐ[R] B) {a : A}
@@ -157,23 +233,47 @@ theorem isAlgebraic_algHom_of_isAlgebraic {B} [Ring B] [Algebra R B] (f : A →
   ⟨p, hp, by rw [aeval_alg_hom, f.comp_apply, ha, map_zero]⟩
 #align is_algebraic_alg_hom_of_is_algebraic isAlgebraic_algHom_of_isAlgebraic
 
+/- warning: alg_equiv.is_algebraic -> AlgEquiv.isAlgebraic is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3)] {B : Type.{u3}} [_inst_8 : Ring.{u3} B] [_inst_9 : Algebra.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B _inst_8)], (AlgEquiv.{u1, u2, u3} R A B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3) (Ring.toSemiring.{u3} B _inst_8) _inst_4 _inst_9) -> (Algebra.IsAlgebraic.{u1, u2} R A _inst_1 _inst_3 _inst_4) -> (Algebra.IsAlgebraic.{u1, u3} R B _inst_1 _inst_8 _inst_9)
+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_3 : Ring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3)] {B : Type.{u1}} [_inst_8 : Ring.{u1} B] [_inst_9 : Algebra.{u2, u1} R B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} B _inst_8)], (AlgEquiv.{u2, u3, u1} R A B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3) (Ring.toSemiring.{u1} B _inst_8) _inst_4 _inst_9) -> (Algebra.IsAlgebraic.{u2, u3} R A _inst_1 _inst_3 _inst_4) -> (Algebra.IsAlgebraic.{u2, u1} R B _inst_1 _inst_8 _inst_9)
+Case conversion may be inaccurate. Consider using '#align alg_equiv.is_algebraic AlgEquiv.isAlgebraicₓ'. -/
 /-- Transfer `algebra.is_algebraic` across an `alg_equiv`. -/
 theorem AlgEquiv.isAlgebraic {B} [Ring B] [Algebra R B] (e : A ≃ₐ[R] B)
     (h : Algebra.IsAlgebraic R A) : Algebra.IsAlgebraic R B := fun b => by
   convert← isAlgebraic_algHom_of_isAlgebraic e.to_alg_hom (h _) <;> apply e.apply_symm_apply
 #align alg_equiv.is_algebraic AlgEquiv.isAlgebraic
 
+/- warning: alg_equiv.is_algebraic_iff -> AlgEquiv.isAlgebraic_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3)] {B : Type.{u3}} [_inst_8 : Ring.{u3} B] [_inst_9 : Algebra.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B _inst_8)], (AlgEquiv.{u1, u2, u3} R A B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3) (Ring.toSemiring.{u3} B _inst_8) _inst_4 _inst_9) -> (Iff (Algebra.IsAlgebraic.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Algebra.IsAlgebraic.{u1, u3} R B _inst_1 _inst_8 _inst_9))
+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_3 : Ring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3)] {B : Type.{u1}} [_inst_8 : Ring.{u1} B] [_inst_9 : Algebra.{u2, u1} R B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} B _inst_8)], (AlgEquiv.{u2, u3, u1} R A B (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A _inst_3) (Ring.toSemiring.{u1} B _inst_8) _inst_4 _inst_9) -> (Iff (Algebra.IsAlgebraic.{u2, u3} R A _inst_1 _inst_3 _inst_4) (Algebra.IsAlgebraic.{u2, u1} R B _inst_1 _inst_8 _inst_9))
+Case conversion may be inaccurate. Consider using '#align alg_equiv.is_algebraic_iff AlgEquiv.isAlgebraic_iffₓ'. -/
 theorem AlgEquiv.isAlgebraic_iff {B} [Ring B] [Algebra R B] (e : A ≃ₐ[R] B) :
     Algebra.IsAlgebraic R A ↔ Algebra.IsAlgebraic R B :=
   ⟨e.IsAlgebraic, e.symm.IsAlgebraic⟩
 #align alg_equiv.is_algebraic_iff AlgEquiv.isAlgebraic_iff
 
+/- warning: is_algebraic_algebra_map_iff -> isAlgebraic_algebraMap_iff is a dubious translation:
+lean 3 declaration is
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(MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} S (AddMonoid.toAddZeroClass.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} S (AddMonoid.toAddZeroClass.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u3} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))))) (Algebra.toModule.{u1, u3} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u2} S A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_3))))))) (SMulWithZero.toSmulZeroClass.{u3, u2} S A (MulZeroClass.toHasZero.{u3} S (MulZeroOneClass.toMulZeroClass.{u3} S (MonoidWithZero.toMulZeroOneClass.{u3} S (Semiring.toMonoidWithZero.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)))))) (AddZeroClass.toHasZero.{u2} A 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(CommRing.toCommSemiring.{u3} S _inst_2) (Ring.toSemiring.{u2} A _inst_3) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_3))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_3))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A 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+Case conversion may be inaccurate. Consider using '#align is_algebraic_algebra_map_iff isAlgebraic_algebraMap_iffₓ'. -/
 theorem isAlgebraic_algebraMap_iff {a : S} (h : Function.Injective (algebraMap S A)) :
     IsAlgebraic R (algebraMap S A a) ↔ IsAlgebraic R a :=
   ⟨fun ⟨p, hp0, hp⟩ => ⟨p, hp0, h (by rwa [map_zero, ← aeval_algebra_map_apply])⟩,
     isAlgebraic_algebraMap_of_isAlgebraic⟩
 #align is_algebraic_algebra_map_iff isAlgebraic_algebraMap_iff
 
+/- warning: is_algebraic_of_pow -> isAlgebraic_of_pow is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3)] {r : A} {n : Nat}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n) -> (IsAlgebraic.{u1, u2} R A _inst_1 _inst_3 _inst_4 (HPow.hPow.{u2, 0, u2} A Nat A (instHPow.{u2, 0} A Nat (Monoid.Pow.{u2} A (Ring.toMonoid.{u2} A _inst_3))) r n)) -> (IsAlgebraic.{u1, u2} R A _inst_1 _inst_3 _inst_4 r)
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3)] {r : A} {n : Nat}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) -> (IsAlgebraic.{u1, u2} R A _inst_1 _inst_3 _inst_4 (HPow.hPow.{u2, 0, u2} A Nat A (instHPow.{u2, 0} A Nat (Monoid.Pow.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A _inst_3))))) r n)) -> (IsAlgebraic.{u1, u2} R A _inst_1 _inst_3 _inst_4 r)
+Case conversion may be inaccurate. Consider using '#align is_algebraic_of_pow isAlgebraic_of_powₓ'. -/
 theorem isAlgebraic_of_pow {r : A} {n : ℕ} (hn : 0 < n) (ht : IsAlgebraic R (r ^ n)) :
     IsAlgebraic R r := by
   obtain ⟨p, p_nonzero, hp⟩ := ht
@@ -182,6 +282,12 @@ theorem isAlgebraic_of_pow {r : A} {n : ℕ} (hn : 0 < n) (ht : IsAlgebraic R (r
   · rwa [Polynomial.expand_aeval n p r]
 #align is_algebraic_of_pow isAlgebraic_of_pow
 
+/- warning: transcendental.pow -> Transcendental.pow is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3)] {r : A}, (Transcendental.{u1, u2} R A _inst_1 _inst_3 _inst_4 r) -> (forall {n : Nat}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n) -> (Transcendental.{u1, u2} R A _inst_1 _inst_3 _inst_4 (HPow.hPow.{u2, 0, u2} A Nat A (instHPow.{u2, 0} A Nat (Monoid.Pow.{u2} A (Ring.toMonoid.{u2} A _inst_3))) r n)))
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : Ring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A _inst_3)] {r : A}, (Transcendental.{u1, u2} R A _inst_1 _inst_3 _inst_4 r) -> (forall {n : Nat}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) -> (Transcendental.{u1, u2} R A _inst_1 _inst_3 _inst_4 (HPow.hPow.{u2, 0, u2} A Nat A (instHPow.{u2, 0} A Nat (Monoid.Pow.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A _inst_3))))) r n)))
+Case conversion may be inaccurate. Consider using '#align transcendental.pow Transcendental.powₓ'. -/
 theorem Transcendental.pow {r : A} (ht : Transcendental R r) {n : ℕ} (hn : 0 < n) :
     Transcendental R (r ^ n) := fun ht' => ht <| isAlgebraic_of_pow hn ht'
 #align transcendental.pow Transcendental.pow
@@ -192,6 +298,7 @@ section Field
 
 variable {K : Type u} {A : Type v} [Field K] [Ring A] [Algebra K A]
 
+#print isAlgebraic_iff_isIntegral /-
 /-- An element of an algebra over a field is algebraic if and only if it is integral.-/
 theorem isAlgebraic_iff_isIntegral {x : A} : IsAlgebraic K x ↔ IsIntegral K x :=
   by
@@ -200,11 +307,14 @@ theorem isAlgebraic_iff_isIntegral {x : A} : IsAlgebraic K x ↔ IsIntegral K x
   refine' ⟨_, monic_mul_leading_coeff_inv hp, _⟩
   rw [← aeval_def, AlgHom.map_mul, hpx, MulZeroClass.zero_mul]
 #align is_algebraic_iff_is_integral isAlgebraic_iff_isIntegral
+-/
 
+#print Algebra.isAlgebraic_iff_isIntegral /-
 protected theorem Algebra.isAlgebraic_iff_isIntegral :
     Algebra.IsAlgebraic K A ↔ Algebra.IsIntegral K A :=
   ⟨fun h x => isAlgebraic_iff_isIntegral.mp (h x), fun h x => isAlgebraic_iff_isIntegral.mpr (h x)⟩
 #align algebra.is_algebraic_iff_is_integral Algebra.isAlgebraic_iff_isIntegral
+-/
 
 end Field
 
@@ -218,6 +328,12 @@ variable [Algebra K L] [Algebra L A] [Algebra K A] [IsScalarTower K L A]
 
 variable [Algebra R S] [Algebra S A] [Algebra R A] [IsScalarTower R S A]
 
+/- warning: algebra.is_algebraic_trans -> Algebra.isAlgebraic_trans is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} {A : Type.{u3}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_5 : CommRing.{u3} A] [_inst_6 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_7 : Algebra.{u2, u3} L A (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))] [_inst_8 : Algebra.{u1, u3} K A (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))] [_inst_9 : IsScalarTower.{u1, u2, u3} K L A (SMulZeroClass.toHasSmul.{u1, u2} K L (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} K L (MulZeroClass.toHasZero.{u1} K (MulZeroOneClass.toMulZeroClass.{u1} K (MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} K L (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (Module.toMulActionWithZero.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6))))) (SMulZeroClass.toHasSmul.{u2, u3} L A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u2, u3} L A (MulZeroClass.toHasZero.{u2} L (MulZeroOneClass.toMulZeroClass.{u2} L (MonoidWithZero.toMulZeroOneClass.{u2} L (Semiring.toMonoidWithZero.{u2} L (CommSemiring.toSemiring.{u2} L (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u2, u3} L A (Semiring.toMonoidWithZero.{u2} L (CommSemiring.toSemiring.{u2} L (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (Module.toMulActionWithZero.{u2, u3} L A (CommSemiring.toSemiring.{u2} L (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))))) (Algebra.toModule.{u2, u3} L A (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)) _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u3} K A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} K A (MulZeroClass.toHasZero.{u1} K (MulZeroOneClass.toMulZeroClass.{u1} K (MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} K A (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (Module.toMulActionWithZero.{u1, u3} K A (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))))) (Algebra.toModule.{u1, u3} K A (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)) _inst_8)))))], (Algebra.IsAlgebraic.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)) _inst_6) -> (Algebra.IsAlgebraic.{u2, u3} L A (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (CommRing.toRing.{u3} A _inst_5) _inst_7) -> (Algebra.IsAlgebraic.{u1, u3} K A (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (CommRing.toRing.{u3} A _inst_5) _inst_8)
+but is expected to have type
+  forall {K : Type.{u3}} {L : Type.{u2}} {A : Type.{u1}} [_inst_1 : Field.{u3} K] [_inst_2 : Field.{u2} L] [_inst_5 : CommRing.{u1} A] [_inst_6 : Algebra.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] [_inst_7 : Algebra.{u2, u1} L A (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))] [_inst_8 : Algebra.{u3, u1} K A (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))] [_inst_9 : IsScalarTower.{u3, u2, u1} K L A (Algebra.toSMul.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6) (Algebra.toSMul.{u2, u1} L A (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)) _inst_7) (Algebra.toSMul.{u3, u1} K A (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)) _inst_8)], (Algebra.IsAlgebraic.{u3, u2} K L (EuclideanDomain.toCommRing.{u3} K (Field.toEuclideanDomain.{u3} K _inst_1)) (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)) _inst_6) -> (Algebra.IsAlgebraic.{u2, u1} L A (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (CommRing.toRing.{u1} A _inst_5) _inst_7) -> (Algebra.IsAlgebraic.{u3, u1} K A (EuclideanDomain.toCommRing.{u3} K (Field.toEuclideanDomain.{u3} K _inst_1)) (CommRing.toRing.{u1} A _inst_5) _inst_8)
+Case conversion may be inaccurate. Consider using '#align algebra.is_algebraic_trans Algebra.isAlgebraic_transₓ'. -/
 /-- If L is an algebraic field extension of K and A is an algebraic algebra over L,
 then A is algebraic over K. -/
 theorem isAlgebraic_trans (L_alg : IsAlgebraic K L) (A_alg : IsAlgebraic L A) : IsAlgebraic K A :=
@@ -228,6 +344,12 @@ theorem isAlgebraic_trans (L_alg : IsAlgebraic K L) (A_alg : IsAlgebraic L A) :
 
 variable (K L)
 
+/- warning: is_algebraic_of_larger_base_of_injective -> isAlgebraic_of_larger_base_of_injective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_3 : CommRing.{u1} R] [_inst_4 : CommRing.{u2} S] [_inst_5 : CommRing.{u3} A] [_inst_10 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_11 : Algebra.{u2, u3} S A (CommRing.toCommSemiring.{u2} S _inst_4) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))] [_inst_12 : Algebra.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_3) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))] [_inst_13 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_10))))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (Module.toMulActionWithZero.{u2, u3} S A (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))))) (Algebra.toModule.{u2, u3} S A (CommRing.toCommSemiring.{u2} S _inst_4) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)) _inst_11))))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_3) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)) _inst_12)))))], (Function.Injective.{succ u1, succ u2} R S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_10))) -> (forall {x : A}, (IsAlgebraic.{u1, u3} R A _inst_3 (CommRing.toRing.{u3} A _inst_5) _inst_12 x) -> (IsAlgebraic.{u2, u3} S A _inst_4 (CommRing.toRing.{u3} A _inst_5) _inst_11 x))
+but is expected to have type
+  forall {R : Type.{u3}} {S : Type.{u2}} {A : Type.{u1}} [_inst_3 : CommRing.{u3} R] [_inst_4 : CommRing.{u2} S] [_inst_5 : CommRing.{u1} A] [_inst_10 : Algebra.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))] [_inst_11 : Algebra.{u2, u1} S A (CommRing.toCommSemiring.{u2} S _inst_4) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))] [_inst_12 : Algebra.{u3, u1} R A (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))] [_inst_13 : IsScalarTower.{u3, u2, u1} R S A (Algebra.toSMul.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) _inst_10) (Algebra.toSMul.{u2, u1} S A (CommRing.toCommSemiring.{u2} S _inst_4) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)) _inst_11) (Algebra.toSMul.{u3, u1} R A (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)) _inst_12)], (Function.Injective.{succ u3, succ u2} R S (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))) R S (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))) R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))) (RingHom.instRingHomClassRingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))))) (algebraMap.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) _inst_10))) -> (forall {x : A}, (IsAlgebraic.{u3, u1} R A _inst_3 (CommRing.toRing.{u1} A _inst_5) _inst_12 x) -> (IsAlgebraic.{u2, u1} S A _inst_4 (CommRing.toRing.{u1} A _inst_5) _inst_11 x))
+Case conversion may be inaccurate. Consider using '#align is_algebraic_of_larger_base_of_injective isAlgebraic_of_larger_base_of_injectiveₓ'. -/
 /-- If x is algebraic over R, then x is algebraic over S when S is an extension of R,
   and the map from `R` to `S` is injective. -/
 theorem isAlgebraic_of_larger_base_of_injective (hinj : Function.Injective (algebraMap R S)) {x : A}
@@ -237,6 +359,12 @@ theorem isAlgebraic_of_larger_base_of_injective (hinj : Function.Injective (alge
     rwa [Ne.def, ← degree_eq_bot, degree_map_eq_of_injective hinj, degree_eq_bot], by simpa⟩
 #align is_algebraic_of_larger_base_of_injective isAlgebraic_of_larger_base_of_injective
 
+/- warning: algebra.is_algebraic_of_larger_base_of_injective -> Algebra.isAlgebraic_of_larger_base_of_injective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_3 : CommRing.{u1} R] [_inst_4 : CommRing.{u2} S] [_inst_5 : CommRing.{u3} A] [_inst_10 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))] [_inst_11 : Algebra.{u2, u3} S A (CommRing.toCommSemiring.{u2} S _inst_4) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))] [_inst_12 : Algebra.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_3) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))] [_inst_13 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_10))))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (Module.toMulActionWithZero.{u2, u3} S A (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))))) (Algebra.toModule.{u2, u3} S A (CommRing.toCommSemiring.{u2} S _inst_4) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)) _inst_11))))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_3) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)) _inst_12)))))], (Function.Injective.{succ u1, succ u2} R S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_3) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_4)) _inst_10))) -> (Algebra.IsAlgebraic.{u1, u3} R A _inst_3 (CommRing.toRing.{u3} A _inst_5) _inst_12) -> (Algebra.IsAlgebraic.{u2, u3} S A _inst_4 (CommRing.toRing.{u3} A _inst_5) _inst_11)
+but is expected to have type
+  forall {R : Type.{u3}} {S : Type.{u2}} {A : Type.{u1}} [_inst_3 : CommRing.{u3} R] [_inst_4 : CommRing.{u2} S] [_inst_5 : CommRing.{u1} A] [_inst_10 : Algebra.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))] [_inst_11 : Algebra.{u2, u1} S A (CommRing.toCommSemiring.{u2} S _inst_4) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))] [_inst_12 : Algebra.{u3, u1} R A (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))] [_inst_13 : IsScalarTower.{u3, u2, u1} R S A (Algebra.toSMul.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) _inst_10) (Algebra.toSMul.{u2, u1} S A (CommRing.toCommSemiring.{u2} S _inst_4) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)) _inst_11) (Algebra.toSMul.{u3, u1} R A (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)) _inst_12)], (Function.Injective.{succ u3, succ u2} R S (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))) R S (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)))) R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))) (RingHom.instRingHomClassRingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4))))))) (algebraMap.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_4)) _inst_10))) -> (Algebra.IsAlgebraic.{u3, u1} R A _inst_3 (CommRing.toRing.{u1} A _inst_5) _inst_12) -> (Algebra.IsAlgebraic.{u2, u1} S A _inst_4 (CommRing.toRing.{u1} A _inst_5) _inst_11)
+Case conversion may be inaccurate. Consider using '#align algebra.is_algebraic_of_larger_base_of_injective Algebra.isAlgebraic_of_larger_base_of_injectiveₓ'. -/
 /-- If A is an algebraic algebra over R, then A is algebraic over S when S is an extension of R,
   and the map from `R` to `S` is injective. -/
 theorem isAlgebraic_of_larger_base_of_injective (hinj : Function.Injective (algebraMap R S))
@@ -244,11 +372,23 @@ theorem isAlgebraic_of_larger_base_of_injective (hinj : Function.Injective (alge
   isAlgebraic_of_larger_base_of_injective hinj (A_alg x)
 #align algebra.is_algebraic_of_larger_base_of_injective Algebra.isAlgebraic_of_larger_base_of_injective
 
+/- warning: is_algebraic_of_larger_base -> isAlgebraic_of_larger_base is a dubious translation:
+lean 3 declaration is
+  forall (K : Type.{u1}) (L : Type.{u2}) {A : Type.{u3}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_5 : CommRing.{u3} A] [_inst_6 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_7 : Algebra.{u2, u3} L A (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))] [_inst_8 : Algebra.{u1, u3} K A (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))] [_inst_9 : IsScalarTower.{u1, u2, u3} K L A (SMulZeroClass.toHasSmul.{u1, u2} K L (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} K L (MulZeroClass.toHasZero.{u1} K (MulZeroOneClass.toMulZeroClass.{u1} K (MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} K L (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (Module.toMulActionWithZero.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6))))) (SMulZeroClass.toHasSmul.{u2, u3} L A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u2, u3} L A (MulZeroClass.toHasZero.{u2} L (MulZeroOneClass.toMulZeroClass.{u2} L (MonoidWithZero.toMulZeroOneClass.{u2} L (Semiring.toMonoidWithZero.{u2} L (CommSemiring.toSemiring.{u2} L (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u2, u3} L A (Semiring.toMonoidWithZero.{u2} L (CommSemiring.toSemiring.{u2} L (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (Module.toMulActionWithZero.{u2, u3} L A (CommSemiring.toSemiring.{u2} L (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))))) (Algebra.toModule.{u2, u3} L A (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)) _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u3} K A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} K A (MulZeroClass.toHasZero.{u1} K (MulZeroOneClass.toMulZeroClass.{u1} K (MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} K A (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (Module.toMulActionWithZero.{u1, u3} K A (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))))) (Algebra.toModule.{u1, u3} K A (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)) _inst_8)))))] {x : A}, (IsAlgebraic.{u1, u3} K A (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (CommRing.toRing.{u3} A _inst_5) _inst_8 x) -> (IsAlgebraic.{u2, u3} L A (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (CommRing.toRing.{u3} A _inst_5) _inst_7 x)
+but is expected to have type
+  forall (K : Type.{u3}) (L : Type.{u1}) {A : Type.{u2}} [_inst_1 : Field.{u3} K] [_inst_2 : Field.{u1} L] [_inst_5 : CommRing.{u2} A] [_inst_6 : Algebra.{u3, u1} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] [_inst_7 : Algebra.{u1, u2} L A (Semifield.toCommSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5))] [_inst_8 : Algebra.{u3, u2} K A (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5))] [_inst_9 : IsScalarTower.{u3, u1, u2} K L A (Algebra.toSMul.{u3, u1} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6) (Algebra.toSMul.{u1, u2} L A (Semifield.toCommSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)) _inst_7) (Algebra.toSMul.{u3, u2} K A (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)) _inst_8)] {x : A}, (IsAlgebraic.{u3, u2} K A (EuclideanDomain.toCommRing.{u3} K (Field.toEuclideanDomain.{u3} K _inst_1)) (CommRing.toRing.{u2} A _inst_5) _inst_8 x) -> (IsAlgebraic.{u1, u2} L A (EuclideanDomain.toCommRing.{u1} L (Field.toEuclideanDomain.{u1} L _inst_2)) (CommRing.toRing.{u2} A _inst_5) _inst_7 x)
+Case conversion may be inaccurate. Consider using '#align is_algebraic_of_larger_base isAlgebraic_of_larger_baseₓ'. -/
 /-- If x is a algebraic over K, then x is algebraic over L when L is an extension of K -/
 theorem isAlgebraic_of_larger_base {x : A} (A_alg : IsAlgebraic K x) : IsAlgebraic L x :=
   isAlgebraic_of_larger_base_of_injective (algebraMap K L).Injective A_alg
 #align is_algebraic_of_larger_base isAlgebraic_of_larger_base
 
+/- warning: algebra.is_algebraic_of_larger_base -> Algebra.isAlgebraic_of_larger_base is a dubious translation:
+lean 3 declaration is
+  forall (K : Type.{u1}) (L : Type.{u2}) {A : Type.{u3}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_5 : CommRing.{u3} A] [_inst_6 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_7 : Algebra.{u2, u3} L A (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))] [_inst_8 : Algebra.{u1, u3} K A (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))] [_inst_9 : IsScalarTower.{u1, u2, u3} K L A (SMulZeroClass.toHasSmul.{u1, u2} K L (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} K L (MulZeroClass.toHasZero.{u1} K (MulZeroOneClass.toMulZeroClass.{u1} K (MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} K L (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (Module.toMulActionWithZero.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6))))) (SMulZeroClass.toHasSmul.{u2, u3} L A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u2, u3} L A (MulZeroClass.toHasZero.{u2} L (MulZeroOneClass.toMulZeroClass.{u2} L (MonoidWithZero.toMulZeroOneClass.{u2} L (Semiring.toMonoidWithZero.{u2} L (CommSemiring.toSemiring.{u2} L (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u2, u3} L A (Semiring.toMonoidWithZero.{u2} L (CommSemiring.toSemiring.{u2} L (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (Module.toMulActionWithZero.{u2, u3} L A (CommSemiring.toSemiring.{u2} L (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))))) (Algebra.toModule.{u2, u3} L A (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)) _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u3} K A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} K A (MulZeroClass.toHasZero.{u1} K (MulZeroOneClass.toMulZeroClass.{u1} K (MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} K A (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)))))))) (Module.toMulActionWithZero.{u1, u3} K A (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5))))) (Algebra.toModule.{u1, u3} K A (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_5)) _inst_8)))))], (Algebra.IsAlgebraic.{u1, u3} K A (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (CommRing.toRing.{u3} A _inst_5) _inst_8) -> (Algebra.IsAlgebraic.{u2, u3} L A (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2)) (CommRing.toRing.{u3} A _inst_5) _inst_7)
+but is expected to have type
+  forall (K : Type.{u3}) (L : Type.{u1}) {A : Type.{u2}} [_inst_1 : Field.{u3} K] [_inst_2 : Field.{u1} L] [_inst_5 : CommRing.{u2} A] [_inst_6 : Algebra.{u3, u1} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] [_inst_7 : Algebra.{u1, u2} L A (Semifield.toCommSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5))] [_inst_8 : Algebra.{u3, u2} K A (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5))] [_inst_9 : IsScalarTower.{u3, u1, u2} K L A (Algebra.toSMul.{u3, u1} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6) (Algebra.toSMul.{u1, u2} L A (Semifield.toCommSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)) _inst_7) (Algebra.toSMul.{u3, u2} K A (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)) _inst_8)], (Algebra.IsAlgebraic.{u3, u2} K A (EuclideanDomain.toCommRing.{u3} K (Field.toEuclideanDomain.{u3} K _inst_1)) (CommRing.toRing.{u2} A _inst_5) _inst_8) -> (Algebra.IsAlgebraic.{u1, u2} L A (EuclideanDomain.toCommRing.{u1} L (Field.toEuclideanDomain.{u1} L _inst_2)) (CommRing.toRing.{u2} A _inst_5) _inst_7)
+Case conversion may be inaccurate. Consider using '#align algebra.is_algebraic_of_larger_base Algebra.isAlgebraic_of_larger_baseₓ'. -/
 /-- If A is an algebraic algebra over K, then A is algebraic over L when L is an extension of K -/
 theorem isAlgebraic_of_larger_base (A_alg : IsAlgebraic K A) : IsAlgebraic L A :=
   isAlgebraic_of_larger_base_of_injective (algebraMap K L).Injective A_alg
@@ -256,11 +396,23 @@ theorem isAlgebraic_of_larger_base (A_alg : IsAlgebraic K A) : IsAlgebraic L A :
 
 variable (K L)
 
+/- warning: algebra.is_integral_of_finite -> Algebra.isIntegral_of_finite is a dubious translation:
+lean 3 declaration is
+  forall (K : Type.{u1}) (L : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_6 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_14 : FiniteDimensional.{u1, u2} K L (Field.toDivisionRing.{u1} K _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6)], Algebra.IsIntegral.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)) _inst_6
+but is expected to have type
+  forall (K : Type.{u2}) (L : Type.{u1}) [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_6 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] [_inst_14 : FiniteDimensional.{u2, u1} K L (Field.toDivisionRing.{u2} K _inst_1) (Ring.toAddCommGroup.{u1} L (DivisionRing.toRing.{u1} L (Field.toDivisionRing.{u1} L _inst_2))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)], Algebra.IsIntegral.{u2, u1} K L (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) (DivisionRing.toRing.{u1} L (Field.toDivisionRing.{u1} L _inst_2)) _inst_6
+Case conversion may be inaccurate. Consider using '#align algebra.is_integral_of_finite Algebra.isIntegral_of_finiteₓ'. -/
 /-- A field extension is integral if it is finite. -/
 theorem isIntegral_of_finite [FiniteDimensional K L] : Algebra.IsIntegral K L := fun x =>
   isIntegral_of_submodule_noetherian ⊤ (IsNoetherian.iff_fg.2 inferInstance) x Algebra.mem_top
 #align algebra.is_integral_of_finite Algebra.isIntegral_of_finite
 
+/- warning: algebra.is_algebraic_of_finite -> Algebra.isAlgebraic_of_finite is a dubious translation:
+lean 3 declaration is
+  forall (K : Type.{u1}) (L : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_6 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [finite : FiniteDimensional.{u1, u2} K L (Field.toDivisionRing.{u1} K _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6)], Algebra.IsAlgebraic.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)) _inst_6
+but is expected to have type
+  forall (K : Type.{u2}) (L : Type.{u1}) [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_6 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] [finite : FiniteDimensional.{u2, u1} K L (Field.toDivisionRing.{u2} K _inst_1) (Ring.toAddCommGroup.{u1} L (DivisionRing.toRing.{u1} L (Field.toDivisionRing.{u1} L _inst_2))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)], Algebra.IsAlgebraic.{u2, u1} K L (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) (DivisionRing.toRing.{u1} L (Field.toDivisionRing.{u1} L _inst_2)) _inst_6
+Case conversion may be inaccurate. Consider using '#align algebra.is_algebraic_of_finite Algebra.isAlgebraic_of_finiteₓ'. -/
 /-- A field extension is algebraic if it is finite. -/
 theorem isAlgebraic_of_finite [finite : FiniteDimensional K L] : IsAlgebraic K L :=
   Algebra.isAlgebraic_iff_isIntegral.mpr (isIntegral_of_finite K L)
@@ -268,6 +420,12 @@ theorem isAlgebraic_of_finite [finite : FiniteDimensional K L] : IsAlgebraic K L
 
 variable {K L}
 
+/- warning: algebra.is_algebraic.alg_hom_bijective -> Algebra.IsAlgebraic.algHom_bijective is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_6 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))], (Algebra.IsAlgebraic.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)) _inst_6) -> (forall (f : AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6), Function.Bijective.{succ u2, succ u2} L L (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) (fun (_x : AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) => L -> L) ([anonymous].{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) f))
+but is expected to have type
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_6 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))], (Algebra.IsAlgebraic.{u2, u1} K L (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) (DivisionRing.toRing.{u1} L (Field.toDivisionRing.{u1} L _inst_2)) _inst_6) -> (forall (f : AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6), Function.Bijective.{succ u1, succ u1} L L (FunLike.coe.{succ u1, succ u1, succ u1} (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : L) => L) _x) (SMulHomClass.toFunLike.{u1, u2, u1, u1} (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) K L L (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6))))) (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u2, u1, u1} (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) K L L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u2, u1, u1} (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) K L L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u1, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6 (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) (AlgHom.algHomClass.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6))))) f))
+Case conversion may be inaccurate. Consider using '#align algebra.is_algebraic.alg_hom_bijective Algebra.IsAlgebraic.algHom_bijectiveₓ'. -/
 theorem IsAlgebraic.algHom_bijective (ha : Algebra.IsAlgebraic K L) (f : L →ₐ[K] L) :
     Function.Bijective f :=
   by
@@ -281,12 +439,24 @@ theorem IsAlgebraic.algHom_bijective (ha : Algebra.IsAlgebraic K L) (f : L →
   exact ⟨a, Subtype.ext_iff.1 ha⟩
 #align algebra.is_algebraic.alg_hom_bijective Algebra.IsAlgebraic.algHom_bijective
 
+/- warning: alg_hom.bijective -> AlgHom.bijective is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_6 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_14 : FiniteDimensional.{u1, u2} K L (Field.toDivisionRing.{u1} K _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6)] (ϕ : AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6), Function.Bijective.{succ u2, succ u2} L L (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) (fun (_x : AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) => L -> L) ([anonymous].{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) ϕ)
+but is expected to have type
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_6 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] [_inst_14 : FiniteDimensional.{u2, u1} K L (Field.toDivisionRing.{u2} K _inst_1) (Ring.toAddCommGroup.{u1} L (DivisionRing.toRing.{u1} L (Field.toDivisionRing.{u1} L _inst_2))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)] (ϕ : AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6), Function.Bijective.{succ u1, succ u1} L L (FunLike.coe.{succ u1, succ u1, succ u1} (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : L) => L) _x) (SMulHomClass.toFunLike.{u1, u2, u1, u1} (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) K L L (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6))))) (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u2, u1, u1} (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) K L L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u2, u1, u1} (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) K L L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u1, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6 (AlgHom.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6) (AlgHom.algHomClass.{u2, u1, u1} K L L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_6 _inst_6))))) ϕ)
+Case conversion may be inaccurate. Consider using '#align alg_hom.bijective AlgHom.bijectiveₓ'. -/
 theorem AlgHom.bijective [FiniteDimensional K L] (ϕ : L →ₐ[K] L) : Function.Bijective ϕ :=
   (Algebra.isAlgebraic_of_finite K L).algHom_bijective ϕ
 #align alg_hom.bijective AlgHom.bijective
 
 variable (K L)
 
+/- warning: algebra.is_algebraic.alg_equiv_equiv_alg_hom -> Algebra.IsAlgebraic.algEquivEquivAlgHom is a dubious translation:
+lean 3 declaration is
+  forall (K : Type.{u1}) (L : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_6 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))], (Algebra.IsAlgebraic.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)) _inst_6) -> (MulEquiv.{u2, u2} (AlgEquiv.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) (AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) (MulOneClass.toHasMul.{u2} (AlgEquiv.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) (Monoid.toMulOneClass.{u2} (AlgEquiv.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) (DivInvMonoid.toMonoid.{u2} (AlgEquiv.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) (Group.toDivInvMonoid.{u2} (AlgEquiv.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) (AlgEquiv.aut.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6))))) (MulOneClass.toHasMul.{u2} (AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) (Monoid.toMulOneClass.{u2} (AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) (AlgHom.End.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6))))
+but is expected to have type
+  forall (K : Type.{u1}) (L : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_6 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))], (Algebra.IsAlgebraic.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)) _inst_6) -> (MulEquiv.{u2, u2} (AlgEquiv.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6 _inst_6) (AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6 _inst_6) (MulOneClass.toMul.{u2} (AlgEquiv.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6 _inst_6) (Monoid.toMulOneClass.{u2} (AlgEquiv.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6 _inst_6) (DivInvMonoid.toMonoid.{u2} (AlgEquiv.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6 _inst_6) (Group.toDivInvMonoid.{u2} (AlgEquiv.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6 _inst_6) (AlgEquiv.aut.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6))))) (MulOneClass.toMul.{u2} (AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6 _inst_6) (Monoid.toMulOneClass.{u2} (AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6 _inst_6) (AlgHom.End.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6))))
+Case conversion may be inaccurate. Consider using '#align algebra.is_algebraic.alg_equiv_equiv_alg_hom Algebra.IsAlgebraic.algEquivEquivAlgHomₓ'. -/
 /-- Bijection between algebra equivalences and algebra homomorphisms -/
 @[simps]
 noncomputable def IsAlgebraic.algEquivEquivAlgHom (ha : Algebra.IsAlgebraic K L) :
@@ -302,6 +472,12 @@ noncomputable def IsAlgebraic.algEquivEquivAlgHom (ha : Algebra.IsAlgebraic K L)
   map_mul' _ _ := rfl
 #align algebra.is_algebraic.alg_equiv_equiv_alg_hom Algebra.IsAlgebraic.algEquivEquivAlgHom
 
+/- warning: alg_equiv_equiv_alg_hom -> algEquivEquivAlgHom is a dubious translation:
+lean 3 declaration is
+  forall (K : Type.{u1}) (L : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_6 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_14 : FiniteDimensional.{u1, u2} K L (Field.toDivisionRing.{u1} K _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6)], MulEquiv.{u2, u2} (AlgEquiv.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) (AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) (MulOneClass.toHasMul.{u2} (AlgEquiv.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) (Monoid.toMulOneClass.{u2} (AlgEquiv.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) (DivInvMonoid.toMonoid.{u2} (AlgEquiv.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) (Group.toDivInvMonoid.{u2} (AlgEquiv.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) (AlgEquiv.aut.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6))))) (MulOneClass.toHasMul.{u2} (AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) (Monoid.toMulOneClass.{u2} (AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6 _inst_6) (AlgHom.End.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6)))
+but is expected to have type
+  forall (K : Type.{u1}) (L : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_6 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] [_inst_14 : FiniteDimensional.{u1, u2} K L (Field.toDivisionRing.{u1} K _inst_1) (Ring.toAddCommGroup.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6)], MulEquiv.{u2, u2} (AlgEquiv.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6 _inst_6) (AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6 _inst_6) (MulOneClass.toMul.{u2} (AlgEquiv.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6 _inst_6) (Monoid.toMulOneClass.{u2} (AlgEquiv.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6 _inst_6) (DivInvMonoid.toMonoid.{u2} (AlgEquiv.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6 _inst_6) (Group.toDivInvMonoid.{u2} (AlgEquiv.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6 _inst_6) (AlgEquiv.aut.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6))))) (MulOneClass.toMul.{u2} (AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6 _inst_6) (Monoid.toMulOneClass.{u2} (AlgHom.{u1, u2, u2} K L L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6 _inst_6) (AlgHom.End.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6)))
+Case conversion may be inaccurate. Consider using '#align alg_equiv_equiv_alg_hom algEquivEquivAlgHomₓ'. -/
 /-- Bijection between algebra equivalences and algebra homomorphisms -/
 @[reducible]
 noncomputable def algEquivEquivAlgHom [FiniteDimensional K L] : (L ≃ₐ[K] L) ≃* (L →ₐ[K] L) :=
@@ -312,6 +488,12 @@ end Algebra
 
 variable {R S : Type _} [CommRing R] [IsDomain R] [CommRing S]
 
+/- warning: exists_integral_multiple -> exists_integral_multiple is a dubious translation:
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+but is expected to have type
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : IsDomain.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))] [_inst_3 : CommRing.{u1} S] [_inst_4 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3))] {z : S}, (IsAlgebraic.{u2, u1} R S _inst_1 (CommRing.toRing.{u1} S _inst_3) _inst_4 z) -> (forall (x : R), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3))))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)) _inst_4) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) _inst_3)))))) -> (Eq.{succ u2} R x (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} R (IsDomain.toCancelCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1) _inst_2))))))) -> (Exists.{succ u1} (Subtype.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)) _inst_4) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)) _inst_4) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)) _inst_4)) x (integralClosure.{u2, u1} R S _inst_1 _inst_3 _inst_4))) (fun (x : Subtype.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)) _inst_4) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)) _inst_4) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)) _inst_4)) x (integralClosure.{u2, u1} R S _inst_1 _inst_3 _inst_4))) => Exists.{succ u2} R (fun (y : R) => Exists.{0} (Ne.{succ u2} R y (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} R (IsDomain.toCancelCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1) _inst_2)))))) (fun (H : Ne.{succ u2} R y (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} R (IsDomain.toCancelCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1) _inst_2)))))) => Eq.{succ u1} S (HMul.hMul.{u1, u1, u1} S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) y) S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_3))))) z (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3))))))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)) _inst_4) y)) (Subtype.val.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) x (SetLike.coe.{u1, u1} (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)) _inst_4) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)) _inst_4) (integralClosure.{u2, u1} R S _inst_1 _inst_3 _inst_4))) x)))))
+Case conversion may be inaccurate. Consider using '#align exists_integral_multiple exists_integral_multipleₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y «expr ≠ » (0 : R)) -/
 theorem exists_integral_multiple [Algebra R S] {z : S} (hz : IsAlgebraic R z)
     (inj : ∀ x, algebraMap R S x = 0 → x = 0) :
@@ -327,6 +509,12 @@ theorem exists_integral_multiple [Algebra R S] {z : S} (hz : IsAlgebraic R z)
   exact ⟨⟨_, x_integral⟩, a, a_ne_zero, rfl⟩
 #align exists_integral_multiple exists_integral_multiple
 
+/- warning: is_integral_closure.exists_smul_eq_mul -> IsIntegralClosure.exists_smul_eq_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : CommRing.{u2} S] {L : Type.{u3}} [_inst_4 : Field.{u3} L] [_inst_5 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3))] [_inst_6 : Algebra.{u2, u3} S L (CommRing.toCommSemiring.{u2} S _inst_3) (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4)))] [_inst_7 : Algebra.{u1, u3} R L (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4)))] [_inst_8 : IsScalarTower.{u1, u2, u3} R S L (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3)) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u3} S L (AddZeroClass.toHasZero.{u3} L (AddMonoid.toAddZeroClass.{u3} L (AddCommMonoid.toAddMonoid.{u3} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L (Semiring.toNonAssocSemiring.{u3} L (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4))))))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S L (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_3)))))) (AddZeroClass.toHasZero.{u3} L (AddMonoid.toAddZeroClass.{u3} L (AddCommMonoid.toAddMonoid.{u3} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L (Semiring.toNonAssocSemiring.{u3} L (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4))))))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S L (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_3))) (AddZeroClass.toHasZero.{u3} L (AddMonoid.toAddZeroClass.{u3} L (AddCommMonoid.toAddMonoid.{u3} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L (Semiring.toNonAssocSemiring.{u3} L (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4))))))))) (Module.toMulActionWithZero.{u2, u3} S L (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L (Semiring.toNonAssocSemiring.{u3} L (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4)))))) (Algebra.toModule.{u2, u3} S L (CommRing.toCommSemiring.{u2} S _inst_3) (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4))) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} R L (AddZeroClass.toHasZero.{u3} L (AddMonoid.toAddZeroClass.{u3} L (AddCommMonoid.toAddMonoid.{u3} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L (Semiring.toNonAssocSemiring.{u3} L (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4))))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R L (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} L (AddMonoid.toAddZeroClass.{u3} L (AddCommMonoid.toAddMonoid.{u3} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L (Semiring.toNonAssocSemiring.{u3} L (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4))))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R L (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} L (AddMonoid.toAddZeroClass.{u3} L (AddCommMonoid.toAddMonoid.{u3} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L (Semiring.toNonAssocSemiring.{u3} L (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4))))))))) (Module.toMulActionWithZero.{u1, u3} R L (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L (Semiring.toNonAssocSemiring.{u3} L (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4)))))) (Algebra.toModule.{u1, u3} R L (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4))) _inst_7)))))] [_inst_9 : IsIntegralClosure.{u2, u1, u3} S R L _inst_1 (CommRing.toCommSemiring.{u2} S _inst_3) (EuclideanDomain.toCommRing.{u3} L (Field.toEuclideanDomain.{u3} L _inst_4)) _inst_7 _inst_6], (Algebra.IsAlgebraic.{u1, u3} R L _inst_1 (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4)) _inst_7) -> (Function.Injective.{succ u1, succ u3} R L (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R L (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} L (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4))))) (fun (_x : RingHom.{u1, u3} R L (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} L (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4))))) => R -> L) (RingHom.hasCoeToFun.{u1, u3} R L (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} L (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4))))) (algebraMap.{u1, u3} R L (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} L (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4))) _inst_7))) -> (forall (a : S) {b : S}, (Ne.{succ u2} S b (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_3)))))))))) -> (Exists.{succ u2} S (fun (c : S) => Exists.{succ u1} R (fun (d : R) => Exists.{0} (Ne.{succ u1} R d (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))) (fun (H : Ne.{succ u1} R d (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))) => Eq.{succ u2} S (SMul.smul.{u1, u2} R S (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_3)) _inst_5))))) d a) (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (Ring.toDistrib.{u2} S (CommRing.toRing.{u2} S _inst_3)))) b c))))))
+but is expected to have type
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : IsDomain.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))] [_inst_3 : CommRing.{u1} S] {L : Type.{u3}} [_inst_4 : Field.{u3} L] [_inst_5 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3))] [_inst_6 : Algebra.{u1, u3} S L (CommRing.toCommSemiring.{u1} S _inst_3) (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_4)))] [_inst_7 : Algebra.{u2, u3} R L (CommRing.toCommSemiring.{u2} R _inst_1) (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_4)))] [_inst_8 : IsScalarTower.{u2, u1, u3} R S L (Algebra.toSMul.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)) _inst_5) (Algebra.toSMul.{u1, u3} S L (CommRing.toCommSemiring.{u1} S _inst_3) (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_4))) _inst_6) (Algebra.toSMul.{u2, u3} R L (CommRing.toCommSemiring.{u2} R _inst_1) (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_4))) _inst_7)] [_inst_9 : IsIntegralClosure.{u1, u2, u3} S R L _inst_1 (CommRing.toCommSemiring.{u1} S _inst_3) (EuclideanDomain.toCommRing.{u3} L (Field.toEuclideanDomain.{u3} L _inst_4)) _inst_7 _inst_6], (Algebra.IsAlgebraic.{u2, u3} R L _inst_1 (DivisionRing.toRing.{u3} L (Field.toDivisionRing.{u3} L _inst_4)) _inst_7) -> (Function.Injective.{succ u2, succ u3} R L (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R L (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} L (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_4))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => L) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R L (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} L (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_4))))) R L (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u3} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L (Semiring.toNonAssocSemiring.{u3} L (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_4)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R L (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} L (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_4))))) R L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L (Semiring.toNonAssocSemiring.{u3} L (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_4))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R L (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} L (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_4))))) R L (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} L (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_4)))) (RingHom.instRingHomClassRingHom.{u2, u3} R L (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} L (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_4)))))))) (algebraMap.{u2, u3} R L (CommRing.toCommSemiring.{u2} R _inst_1) (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_4))) _inst_7))) -> (forall (a : S) {b : S}, (Ne.{succ u1} S b (OfNat.ofNat.{u1} S 0 (Zero.toOfNat0.{u1} S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)))))) -> (Exists.{succ u1} S (fun (c : S) => Exists.{succ u2} R (fun (d : R) => Exists.{0} (Ne.{succ u2} R d (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} R (IsDomain.toCancelCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1) _inst_2)))))) (fun (H : Ne.{succ u2} R d (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} R (IsDomain.toCancelCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1) _inst_2)))))) => Eq.{succ u1} S (HSMul.hSMul.{u2, u1, u1} R S S (instHSMul.{u2, u1} R S (Algebra.toSMul.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)) _inst_5)) d a) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_3))))) b c))))))
+Case conversion may be inaccurate. Consider using '#align is_integral_closure.exists_smul_eq_mul IsIntegralClosure.exists_smul_eq_mulₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (d «expr ≠ » (0 : R)) -/
 /-- A fraction `(a : S) / (b : S)` can be reduced to `(c : S) / (d : R)`,
 if `S` is the integral closure of `R` in an algebraic extension `L` of `R`. -/
@@ -350,6 +538,12 @@ section Field
 
 variable {K L : Type _} [Field K] [Field L] [Algebra K L] (A : Subalgebra K L)
 
+/- warning: inv_eq_of_aeval_div_X_ne_zero -> inv_eq_of_aeval_divX_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_4 : Field.{u1} K] [_inst_5 : Field.{u2} L] [_inst_6 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5)))] {x : L} {p : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_4)))}, (Ne.{succ u2} L (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) _inst_6) (fun (_x : AlgHom.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) _inst_6) => 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+but is expected to have type
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_4 : Field.{u2} K] [_inst_5 : Field.{u1} L] [_inst_6 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))] {x : L} {p : Polynomial.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))}, (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) (Polynomial.divX.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L 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(Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))))) (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6 (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6))))) (Polynomial.aeval.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6 x) (Polynomial.divX.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) (Polynomial.divX.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) (Polynomial.divX.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p)) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) (Polynomial.divX.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p)) (CommGroupWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) (Polynomial.divX.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p)) (Semifield.toCommGroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) (Polynomial.divX.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K 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(Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} 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(CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) 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_inst_4)))) _inst_6 (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K 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=> L) p) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) p) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) => L) p) _inst_5)))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K 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(Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))))) (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6 (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6))))) (Polynomial.aeval.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6 x) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (RingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) K L (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (NonUnitalNonAssocSemiring.toMul.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))) (RingHom.instRingHomClassRingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (algebraMap.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6) (Polynomial.coeff.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))
+Case conversion may be inaccurate. Consider using '#align inv_eq_of_aeval_div_X_ne_zero inv_eq_of_aeval_divX_ne_zeroₓ'. -/
 theorem inv_eq_of_aeval_divX_ne_zero {x : L} {p : K[X]} (aeval_ne : aeval x (divX p) ≠ 0) :
     x⁻¹ = aeval x (divX p) / (aeval x p - algebraMap _ _ (p.coeff 0)) :=
   by
@@ -359,6 +553,12 @@ theorem inv_eq_of_aeval_divX_ne_zero {x : L} {p : K[X]} (aeval_ne : aeval x (div
   exact aeval_ne
 #align inv_eq_of_aeval_div_X_ne_zero inv_eq_of_aeval_divX_ne_zero
 
+/- warning: inv_eq_of_root_of_coeff_zero_ne_zero -> inv_eq_of_root_of_coeff_zero_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_4 : Field.{u1} K] [_inst_5 : Field.{u2} L] [_inst_6 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5)))] {x : L} {p : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_4)))}, (Eq.{succ u2} L (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K 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+but is expected to have type
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u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (SMulZeroClass.toSMul.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (AddMonoid.toZero.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))))) (DistribSMul.toSMulZeroClass.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))))) (DistribMulAction.toDistribSMul.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))))) (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K 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(Field.toSemifield.{u1} L _inst_5))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K 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_inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) (Module.toDistribMulAction.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))))) (Algebra.toModule.{u2, u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6 (AlgHom.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} K (Polynomial.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (Polynomial.semiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) (Polynomial.algebraOfAlgebra.{u2, u2} K K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (Algebra.id.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) _inst_6))))) (Polynomial.aeval.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6 x) (Polynomial.divX.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) p)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (RingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) K L (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))))) (NonUnitalNonAssocSemiring.toMul.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))))) K L (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K 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+Case conversion may be inaccurate. Consider using '#align inv_eq_of_root_of_coeff_zero_ne_zero inv_eq_of_root_of_coeff_zero_ne_zeroₓ'. -/
 theorem inv_eq_of_root_of_coeff_zero_ne_zero {x : L} {p : K[X]} (aeval_eq : aeval x p = 0)
     (coeff_zero_ne : p.coeff 0 ≠ 0) : x⁻¹ = -(aeval x (divX p) / algebraMap _ _ (p.coeff 0)) :=
   by
@@ -370,6 +570,12 @@ theorem inv_eq_of_root_of_coeff_zero_ne_zero {x : L} {p : K[X]} (aeval_eq : aeva
   rw [AlgHom.map_add, AlgHom.map_mul, h, MulZeroClass.zero_mul, zero_add, aeval_C]
 #align inv_eq_of_root_of_coeff_zero_ne_zero inv_eq_of_root_of_coeff_zero_ne_zero
 
+/- warning: subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero -> Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_4 : Field.{u1} K] [_inst_5 : Field.{u2} L] [_inst_6 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5)))] (A : Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6) {x : coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6)) A} {p : Polynomial.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_4)))}, (Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6)) A) (coeFn.{max (succ 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(Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6 A) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6 A)) (fun (_x : AlgHom.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} K 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L _inst_5))) _inst_6 A) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6 A)) => (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) -> (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6)) A)) ([anonymous].{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6) L (Subalgebra.setLike.{u1, u2} K L 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+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_4 : Field.{u1} K] [_inst_5 : Field.{u2} L] [_inst_6 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5)))] (A : Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) {x : Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)} {p : Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))}, (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) => Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K 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(Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))))))) (Module.toDistribMulAction.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))))) (Algebra.toModule.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))))))) (SMulZeroClass.toSMul.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (AddMonoid.toZero.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)))))) (DistribSMul.toSMulZeroClass.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)))))) (DistribMulAction.toDistribSMul.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)))) (Algebra.toModule.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)) K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A))))) (Module.toDistribMulAction.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))))) (Algebra.toModule.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)))) (Algebra.toModule.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)) K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A))) (Module.toDistribMulAction.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))))) (Algebra.toModule.{u1, u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)))) (Algebra.toModule.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K 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(Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)) (AlgHom.algHomClass.{u1, u1, u2} K (Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Polynomial.semiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Polynomial.algebraOfAlgebra.{u1, u1} K K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (Algebra.id.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A)))))) (Polynomial.aeval.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6 A) x) p) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) => Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) p) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) => Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)) p) (ZeroMemClass.zero.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (CommMonoidWithZero.toZero.{u2} L (CommGroupWithZero.toCommMonoidWithZero.{u2} L (Semifield.toCommGroupWithZero.{u2} L (Field.toSemifield.{u2} L _inst_5)))) (AddSubmonoidClass.toZeroMemClass.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (AddMonoid.toAddZeroClass.{u2} L (AddMonoidWithOne.toAddMonoid.{u2} L (AddGroupWithOne.toAddMonoidWithOne.{u2} L (Ring.toAddGroupWithOne.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5)))))) (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SubsemiringClass.toAddSubmonoidClass.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5)))) (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (Subalgebra.SubsemiringClass.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6))) A)))) -> (Ne.{succ u1} K (Polynomial.coeff.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) p (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_4))))))) -> (Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) (Inv.inv.{u2} L (Field.toInv.{u2} L _inst_5) (Subtype.val.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Set.{u2} L) (Set.instMembershipSet.{u2} L) x (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) A)) x)) A)
+Case conversion may be inaccurate. Consider using '#align subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zeroₓ'. -/
 theorem Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero {x : A} {p : K[X]}
     (aeval_eq : aeval x p = 0) (coeff_zero_ne : p.coeff 0 ≠ 0) : (x⁻¹ : L) ∈ A :=
   by
@@ -382,6 +588,12 @@ theorem Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero {x : A} {p : K[X]}
     map_inv₀, map_neg, inv_neg, neg_mul, Subalgebra.aeval_coe]
 #align subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero
 
+/- warning: subalgebra.inv_mem_of_algebraic -> Subalgebra.inv_mem_of_algebraic is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_4 : Field.{u1} K] [_inst_5 : Field.{u2} L] [_inst_6 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5)))] (A : Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) {x : Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) x A)}, (IsAlgebraic.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5)) _inst_6 (Subtype.val.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Set.{u2} L) (Set.instMembershipSet.{u2} L) x (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) A)) x)) -> (Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6)) (Inv.inv.{u2} L (Field.toInv.{u2} L _inst_5) (Subtype.val.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Set.{u2} L) (Set.instMembershipSet.{u2} L) x (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_5))) _inst_6) A)) x)) A)
+Case conversion may be inaccurate. Consider using '#align subalgebra.inv_mem_of_algebraic Subalgebra.inv_mem_of_algebraicₓ'. -/
 theorem Subalgebra.inv_mem_of_algebraic {x : A} (hx : IsAlgebraic K (x : L)) : (x⁻¹ : L) ∈ A :=
   by
   obtain ⟨p, ne_zero, aeval_eq⟩ := hx
@@ -401,6 +613,12 @@ theorem Subalgebra.inv_mem_of_algebraic {x : A} (hx : IsAlgebraic K (x : L)) : (
       exact A.zero_mem
 #align subalgebra.inv_mem_of_algebraic Subalgebra.inv_mem_of_algebraic
 
+/- warning: subalgebra.is_field_of_algebraic -> Subalgebra.isField_of_algebraic is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_4 : Field.{u1} K] [_inst_5 : Field.{u2} L] [_inst_6 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5)))] (A : Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6), (Algebra.IsAlgebraic.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5)) _inst_6) -> (IsField.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6)) A) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_5))) _inst_6 A))
+but is expected to have type
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_4 : Field.{u2} K] [_inst_5 : Field.{u1} L] [_inst_6 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5)))] (A : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6), (Algebra.IsAlgebraic.{u2, u1} K L (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) (DivisionRing.toRing.{u1} L (Field.toDivisionRing.{u1} L _inst_5)) _inst_6) -> (IsField.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6) L (Subalgebra.instSetLikeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6)) x A)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_5))) _inst_6 A))
+Case conversion may be inaccurate. Consider using '#align subalgebra.is_field_of_algebraic Subalgebra.isField_of_algebraicₓ'. -/
 /-- In an algebraic extension L/K, an intermediate subalgebra is a field. -/
 theorem Subalgebra.isField_of_algebraic (hKL : Algebra.IsAlgebraic K L) : IsField A :=
   { show Nontrivial A by infer_instance, Subalgebra.toCommRing A with
@@ -415,43 +633,52 @@ section Pi
 
 variable (R' : Type u) (S' : Type v) (T' : Type w)
 
+#print Polynomial.hasSMulPi /-
 /-- This is not an instance as it forms a diamond with `pi.has_smul`.
 
 See the `instance_diamonds` test for details. -/
-def Polynomial.hasSmulPi [Semiring R'] [SMul R' S'] : SMul R'[X] (R' → S') :=
+def Polynomial.hasSMulPi [Semiring R'] [SMul R' S'] : SMul R'[X] (R' → S') :=
   ⟨fun p f x => eval x p • f x⟩
-#align polynomial.has_smul_pi Polynomial.hasSmulPi
+#align polynomial.has_smul_pi Polynomial.hasSMulPi
+-/
 
+#print Polynomial.hasSMulPi' /-
 /-- This is not an instance as it forms a diamond with `pi.has_smul`.
 
 See the `instance_diamonds` test for details. -/
-noncomputable def Polynomial.hasSmulPi' [CommSemiring R'] [Semiring S'] [Algebra R' S']
+noncomputable def Polynomial.hasSMulPi' [CommSemiring R'] [Semiring S'] [Algebra R' S']
     [SMul S' T'] : SMul R'[X] (S' → T') :=
   ⟨fun p f x => aeval x p • f x⟩
-#align polynomial.has_smul_pi' Polynomial.hasSmulPi'
+#align polynomial.has_smul_pi' Polynomial.hasSMulPi'
+-/
 
 variable {R} {S}
 
-attribute [local instance] Polynomial.hasSmulPi Polynomial.hasSmulPi'
+attribute [local instance] Polynomial.hasSMulPi Polynomial.hasSMulPi'
 
+#print polynomial_smul_apply /-
 @[simp]
 theorem polynomial_smul_apply [Semiring R'] [SMul R' S'] (p : R'[X]) (f : R' → S') (x : R') :
     (p • f) x = eval x p • f x :=
   rfl
 #align polynomial_smul_apply polynomial_smul_apply
+-/
 
+#print polynomial_smul_apply' /-
 @[simp]
 theorem polynomial_smul_apply' [CommSemiring R'] [Semiring S'] [Algebra R' S'] [SMul S' T']
     (p : R'[X]) (f : S' → T') (x : S') : (p • f) x = aeval x p • f x :=
   rfl
 #align polynomial_smul_apply' polynomial_smul_apply'
+-/
 
 variable [CommSemiring R'] [CommSemiring S'] [CommSemiring T'] [Algebra R' S'] [Algebra S' T']
 
+#print Polynomial.algebraPi /-
 /-- This is not an instance for the same reasons as `polynomial.has_smul_pi'`. -/
 noncomputable def Polynomial.algebraPi : Algebra R'[X] (S' → T') :=
   {
-    Polynomial.hasSmulPi' R' S'
+    Polynomial.hasSMulPi' R' S'
       T' with
     toFun := fun p z => algebraMap S' T' (aeval z p)
     map_one' := funext fun z => by simp only [Polynomial.aeval_one, Pi.one_apply, map_one]
@@ -465,15 +692,28 @@ noncomputable def Polynomial.algebraPi : Algebra R'[X] (S' → T') :=
         simp only [Algebra.algebraMap_eq_smul_one, polynomial_smul_apply', one_mul, Pi.mul_apply,
           Algebra.smul_mul_assoc] }
 #align polynomial.algebra_pi Polynomial.algebraPi
+-/
 
 attribute [local instance] Polynomial.algebraPi
 
+/- warning: polynomial.algebra_map_pi_eq_aeval -> Polynomial.algebraMap_pi_eq_aeval is a dubious translation:
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(Algebra.id.{u1} R' _inst_4)) _inst_7))))) (Polynomial.aeval.{u1, u2} R' S' _inst_4 (CommSemiring.toSemiring.{u2} S' _inst_5) _inst_7 z) p))
+Case conversion may be inaccurate. Consider using '#align polynomial.algebra_map_pi_eq_aeval Polynomial.algebraMap_pi_eq_aevalₓ'. -/
 @[simp]
 theorem Polynomial.algebraMap_pi_eq_aeval :
     (algebraMap R'[X] (S' → T') : R'[X] → S' → T') = fun p z => algebraMap _ _ (aeval z p) :=
   rfl
 #align polynomial.algebra_map_pi_eq_aeval Polynomial.algebraMap_pi_eq_aeval
 
+/- warning: polynomial.algebra_map_pi_self_eq_eval -> Polynomial.algebraMap_pi_self_eq_eval is a dubious translation:
+lean 3 declaration is
+  forall (R' : Type.{u1}) [_inst_4 : CommSemiring.{u1} R'], Eq.{succ u1} ((fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (R' -> R') (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.commSemiring.{u1} R' _inst_4))) (Semiring.toNonAssocSemiring.{u1} (R' -> R') (Pi.semiring.{u1, u1} R' (fun (ᾰ : R') => R') (fun (i : R') => CommSemiring.toSemiring.{u1} R' _inst_4)))) => (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) -> R' -> R') (algebraMap.{u1, u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (R' -> R') (Polynomial.commSemiring.{u1} R' _inst_4) (Pi.semiring.{u1, u1} R' (fun (ᾰ : R') => R') (fun (i : R') => CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.algebraPi.{u1, u1, u1} R' R' R' _inst_4 _inst_4 _inst_4 (Algebra.id.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (R' -> R') (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.commSemiring.{u1} R' _inst_4))) (Semiring.toNonAssocSemiring.{u1} (R' -> R') (Pi.semiring.{u1, u1} R' (fun (ᾰ : R') => R') (fun (i : R') => CommSemiring.toSemiring.{u1} R' _inst_4)))) (fun (_x : RingHom.{u1, u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (R' -> R') (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.commSemiring.{u1} R' _inst_4))) (Semiring.toNonAssocSemiring.{u1} (R' -> R') (Pi.semiring.{u1, u1} R' (fun (ᾰ : R') => R') (fun (i : R') => CommSemiring.toSemiring.{u1} R' _inst_4)))) => (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) -> R' -> R') (RingHom.hasCoeToFun.{u1, u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (R' -> R') (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.commSemiring.{u1} R' _inst_4))) (Semiring.toNonAssocSemiring.{u1} (R' -> R') (Pi.semiring.{u1, u1} R' (fun (ᾰ : R') => R') (fun (i : R') => CommSemiring.toSemiring.{u1} R' _inst_4)))) (algebraMap.{u1, u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (R' -> R') (Polynomial.commSemiring.{u1} R' _inst_4) (Pi.semiring.{u1, u1} R' (fun (ᾰ : R') => R') (fun (i : R') => CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.algebraPi.{u1, u1, u1} R' R' R' _inst_4 _inst_4 _inst_4 (Algebra.id.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)))) (fun (p : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (z : R') => Polynomial.eval.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4) z p)
+but is expected to have type
+  forall (R' : Type.{u1}) [_inst_4 : CommSemiring.{u1} R'], Eq.{succ u1} (forall (a : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => R' -> R') a) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (R' -> R') (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.commSemiring.{u1} R' _inst_4))) (Semiring.toNonAssocSemiring.{u1} (R' -> R') (Pi.semiring.{u1, u1} R' (fun (a._@.Mathlib.RingTheory.Algebraic._hyg.5731 : R') => R') (fun (i : R') => CommSemiring.toSemiring.{u1} R' _inst_4)))) (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (fun (_x : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) => R' -> R') _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (R' -> R') (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.commSemiring.{u1} R' _inst_4))) (Semiring.toNonAssocSemiring.{u1} (R' -> R') (Pi.semiring.{u1, u1} R' (fun (a._@.Mathlib.RingTheory.Algebraic._hyg.5731 : R') => R') (fun (i : R') => CommSemiring.toSemiring.{u1} R' _inst_4)))) (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (R' -> R') (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.commSemiring.{u1} R' _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} (R' -> R') (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (R' -> R') (Semiring.toNonAssocSemiring.{u1} (R' -> R') (Pi.semiring.{u1, u1} R' (fun (a._@.Mathlib.RingTheory.Algebraic._hyg.5731 : R') => R') (fun (i : R') => CommSemiring.toSemiring.{u1} R' _inst_4))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (R' -> R') (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.commSemiring.{u1} R' _inst_4))) (Semiring.toNonAssocSemiring.{u1} (R' -> R') (Pi.semiring.{u1, u1} R' (fun (a._@.Mathlib.RingTheory.Algebraic._hyg.5731 : R') => R') (fun (i : R') => CommSemiring.toSemiring.{u1} R' _inst_4)))) (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (R' -> R') (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.commSemiring.{u1} R' _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (R' -> R') (Semiring.toNonAssocSemiring.{u1} (R' -> R') (Pi.semiring.{u1, u1} R' (fun (a._@.Mathlib.RingTheory.Algebraic._hyg.5731 : R') => R') (fun (i : R') => CommSemiring.toSemiring.{u1} R' _inst_4)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (R' -> R') (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.commSemiring.{u1} R' _inst_4))) (Semiring.toNonAssocSemiring.{u1} (R' -> R') (Pi.semiring.{u1, u1} R' (fun (a._@.Mathlib.RingTheory.Algebraic._hyg.5731 : R') => R') (fun (i : R') => CommSemiring.toSemiring.{u1} R' _inst_4)))) (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (R' -> R') (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.commSemiring.{u1} R' _inst_4))) (Semiring.toNonAssocSemiring.{u1} (R' -> R') (Pi.semiring.{u1, u1} R' (fun (a._@.Mathlib.RingTheory.Algebraic._hyg.5731 : R') => R') (fun (i : R') => CommSemiring.toSemiring.{u1} R' _inst_4))) (RingHom.instRingHomClassRingHom.{u1, u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (R' -> R') (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.commSemiring.{u1} R' _inst_4))) (Semiring.toNonAssocSemiring.{u1} (R' -> R') (Pi.semiring.{u1, u1} R' (fun (a._@.Mathlib.RingTheory.Algebraic._hyg.5731 : R') => R') (fun (i : R') => CommSemiring.toSemiring.{u1} R' _inst_4))))))) (algebraMap.{u1, u1} (Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (R' -> R') (Polynomial.commSemiring.{u1} R' _inst_4) (Pi.semiring.{u1, u1} R' (fun (ᾰ : R') => R') (fun (i : R') => CommSemiring.toSemiring.{u1} R' _inst_4)) (Polynomial.algebraPi.{u1, u1, u1} R' R' R' _inst_4 _inst_4 _inst_4 (Algebra.id.{u1} R' _inst_4) (Algebra.id.{u1} R' _inst_4)))) (fun (p : Polynomial.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4)) (z : R') => Polynomial.eval.{u1} R' (CommSemiring.toSemiring.{u1} R' _inst_4) z p)
+Case conversion may be inaccurate. Consider using '#align polynomial.algebra_map_pi_self_eq_eval Polynomial.algebraMap_pi_self_eq_evalₓ'. -/
 @[simp]
 theorem Polynomial.algebraMap_pi_self_eq_eval :
     (algebraMap R'[X] (R' → R') : R'[X] → R' → R') = fun p z => eval z p :=

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

@@ -160,7 +160,7 @@ theorem isAlgebraic_algHom_of_isAlgebraic {B} [Ring B] [Algebra R B] (f : A →
 /-- Transfer `algebra.is_algebraic` across an `alg_equiv`. -/
 theorem AlgEquiv.isAlgebraic {B} [Ring B] [Algebra R B] (e : A ≃ₐ[R] B)
     (h : Algebra.IsAlgebraic R A) : Algebra.IsAlgebraic R B := fun b => by
-  convert ← isAlgebraic_algHom_of_isAlgebraic e.to_alg_hom (h _) <;> apply e.apply_symm_apply
+  convert← isAlgebraic_algHom_of_isAlgebraic e.to_alg_hom (h _) <;> apply e.apply_symm_apply
 #align alg_equiv.is_algebraic AlgEquiv.isAlgebraic
 
 theorem AlgEquiv.isAlgebraic_iff {B} [Ring B] [Algebra R B] (e : A ≃ₐ[R] B) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/2196ab363eb097c008d4497125e0dde23fb36db2

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 
 ! This file was ported from Lean 3 source module ring_theory.algebraic
-! leanprover-community/mathlib commit 3d32bf9cef95940e3fe1ca0dd2412e0f21579f46
+! leanprover-community/mathlib commit 2196ab363eb097c008d4497125e0dde23fb36db2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -353,7 +353,7 @@ variable {K L : Type _} [Field K] [Field L] [Algebra K L] (A : Subalgebra K L)
 theorem inv_eq_of_aeval_divX_ne_zero {x : L} {p : K[X]} (aeval_ne : aeval x (divX p) ≠ 0) :
     x⁻¹ = aeval x (divX p) / (aeval x p - algebraMap _ _ (p.coeff 0)) :=
   by
-  rw [inv_eq_iff_inv_eq, inv_div, div_eq_iff, sub_eq_iff_eq_add, mul_comm]
+  rw [inv_eq_iff_eq_inv, inv_div, eq_comm, div_eq_iff, sub_eq_iff_eq_add, mul_comm]
   conv_lhs => rw [← div_X_mul_X_add p]
   rw [AlgHom.map_add, AlgHom.map_mul, aeval_X, aeval_C]
   exact aeval_ne

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

@@ -105,7 +105,7 @@ theorem IsIntegral.isAlgebraic [Nontrivial R] {x : A} : IsIntegral R x → IsAlg
 variable {R}
 
 theorem isAlgebraic_zero [Nontrivial R] : IsAlgebraic R (0 : A) :=
-  ⟨_, X_ne_zero, aeval_x 0⟩
+  ⟨_, X_ne_zero, aeval_X 0⟩
 #align is_algebraic_zero isAlgebraic_zero
 
 /-- An element of `R` is algebraic, when viewed as an element of the `R`-algebra `A`. -/

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

@@ -198,7 +198,7 @@ theorem isAlgebraic_iff_isIntegral {x : A} : IsAlgebraic K x ↔ IsIntegral K x
   refine' ⟨_, IsIntegral.isAlgebraic K⟩
   rintro ⟨p, hp, hpx⟩
   refine' ⟨_, monic_mul_leading_coeff_inv hp, _⟩
-  rw [← aeval_def, AlgHom.map_mul, hpx, zero_mul]
+  rw [← aeval_def, AlgHom.map_mul, hpx, MulZeroClass.zero_mul]
 #align is_algebraic_iff_is_integral isAlgebraic_iff_isIntegral
 
 protected theorem Algebra.isAlgebraic_iff_isIntegral :
@@ -367,7 +367,7 @@ theorem inv_eq_of_root_of_coeff_zero_ne_zero {x : L} {p : K[X]} (aeval_eq : aeva
   rw [RingHom.map_zero]
   convert aeval_eq
   conv_rhs => rw [← div_X_mul_X_add p]
-  rw [AlgHom.map_add, AlgHom.map_mul, h, zero_mul, zero_add, aeval_C]
+  rw [AlgHom.map_add, AlgHom.map_mul, h, MulZeroClass.zero_mul, zero_add, aeval_C]
 #align inv_eq_of_root_of_coeff_zero_ne_zero inv_eq_of_root_of_coeff_zero_ne_zero
 
 theorem Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero {x : A} {p : K[X]}

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

@@ -110,7 +110,7 @@ theorem isAlgebraic_zero [Nontrivial R] : IsAlgebraic R (0 : A) :=
 
 /-- An element of `R` is algebraic, when viewed as an element of the `R`-algebra `A`. -/
 theorem isAlgebraic_algebraMap [Nontrivial R] (x : R) : IsAlgebraic R (algebraMap R A x) :=
-  ⟨_, x_sub_c_ne_zero x, by rw [_root_.map_sub, aeval_X, aeval_C, sub_self]⟩
+  ⟨_, X_sub_C_ne_zero x, by rw [_root_.map_sub, aeval_X, aeval_C, sub_self]⟩
 #align is_algebraic_algebra_map isAlgebraic_algebraMap
 
 theorem isAlgebraic_one [Nontrivial R] : IsAlgebraic R (1 : A) :=

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

@@ -105,7 +105,7 @@ theorem IsIntegral.isAlgebraic [Nontrivial R] {x : A} : IsIntegral R x → IsAlg
 variable {R}
 
 theorem isAlgebraic_zero [Nontrivial R] : IsAlgebraic R (0 : A) :=
-  ⟨_, x_ne_zero, aeval_x 0⟩
+  ⟨_, X_ne_zero, aeval_x 0⟩
 #align is_algebraic_zero isAlgebraic_zero
 
 /-- An element of `R` is algebraic, when viewed as an element of the `R`-algebra `A`. -/

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

@@ -312,7 +312,7 @@ end Algebra
 
 variable {R S : Type _} [CommRing R] [IsDomain R] [CommRing S]
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (y «expr ≠ » (0 : R)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y «expr ≠ » (0 : R)) -/
 theorem exists_integral_multiple [Algebra R S] {z : S} (hz : IsAlgebraic R z)
     (inj : ∀ x, algebraMap R S x = 0 → x = 0) :
     ∃ (x : integralClosure R S)(y : _)(_ : y ≠ (0 : R)), z * algebraMap R S y = x :=
@@ -327,7 +327,7 @@ theorem exists_integral_multiple [Algebra R S] {z : S} (hz : IsAlgebraic R z)
   exact ⟨⟨_, x_integral⟩, a, a_ne_zero, rfl⟩
 #align exists_integral_multiple exists_integral_multiple
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (d «expr ≠ » (0 : R)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (d «expr ≠ » (0 : R)) -/
 /-- A fraction `(a : S) / (b : S)` can be reduced to `(c : S) / (d : R)`,
 if `S` is the integral closure of `R` in an algebraic extension `L` of `R`. -/
 theorem IsIntegralClosure.exists_smul_eq_mul {L : Type _} [Field L] [Algebra R S] [Algebra S L]

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

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

@@ -91,7 +91,7 @@ variable {R : Type u} {S : Type*} {A : Type v} [CommRing R]
 variable [CommRing S] [Ring A] [Algebra R A] [Algebra R S] [Algebra S A]
 variable [IsScalarTower R S A]
 
-/-- An integral element of an algebra is algebraic.-/
+/-- An integral element of an algebra is algebraic. -/
 theorem IsIntegral.isAlgebraic [Nontrivial R] {x : A} : IsIntegral R x → IsAlgebraic R x :=
   fun ⟨p, hp, hpx⟩ => ⟨p, hp.ne_zero, hpx⟩
 #align is_integral.is_algebraic IsIntegral.isAlgebraic
@@ -216,7 +216,7 @@ section Field
 
 variable {K : Type u} {A : Type v} [Field K] [Ring A] [Algebra K A]
 
-/-- An element of an algebra over a field is algebraic if and only if it is integral.-/
+/-- An element of an algebra over a field is algebraic if and only if it is integral. -/
 theorem isAlgebraic_iff_isIntegral {x : A} : IsAlgebraic K x ↔ IsIntegral K x := by
   refine' ⟨_, IsIntegral.isAlgebraic⟩
   rintro ⟨p, hp, hpx⟩

@@ -252,7 +252,7 @@ theorem IsAlgebraic.tower_top_of_injective
     (A_alg : IsAlgebraic R x) : IsAlgebraic S x :=
   let ⟨p, hp₁, hp₂⟩ := A_alg
   ⟨p.map (algebraMap _ _), by
-    rwa [Ne.def, ← degree_eq_bot, degree_map_eq_of_injective hinj, degree_eq_bot], by simpa⟩
+    rwa [Ne, ← degree_eq_bot, degree_map_eq_of_injective hinj, degree_eq_bot], by simpa⟩
 #align is_algebraic_of_larger_base_of_injective IsAlgebraic.tower_top_of_injective
 
 /-- If A is an algebraic algebra over R, then A is algebraic over S when S is an extension of R,

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

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

| Statement | New name | Old name | |

@@ -412,7 +412,7 @@ theorem IsIntegralClosure.exists_smul_eq_mul {L : Type*} [Field L] [Algebra R S]
     ⟨IsIntegralClosure.mk' S (c : L) c.2, d, d_ne, IsIntegralClosure.algebraMap_injective S R L _⟩
   simp only [Algebra.smul_def, RingHom.map_mul, IsIntegralClosure.algebraMap_mk', ← hx, ←
     IsScalarTower.algebraMap_apply]
-  rw [← mul_assoc _ (_ / _), mul_div_cancel' (algebraMap S L a), mul_comm]
+  rw [← mul_assoc _ (_ / _), mul_div_cancel₀ (algebraMap S L a), mul_comm]
   exact mt ((injective_iff_map_eq_zero _).mp (IsIntegralClosure.algebraMap_injective S R L) _) hb
 #align is_integral_closure.exists_smul_eq_mul IsIntegralClosure.exists_smul_eq_mul
 

@@ -389,7 +389,7 @@ variable {R S : Type*} [CommRing R] [IsDomain R] [CommRing S]
 
 theorem exists_integral_multiple [Algebra R S] {z : S} (hz : IsAlgebraic R z)
     (inj : ∀ x, algebraMap R S x = 0 → x = 0) :
-    ∃ (x : integralClosure R S) (y : _) (_ : y ≠ (0 : R)), z * algebraMap R S y = x := by
+    ∃ᵉ (x : integralClosure R S) (y ≠ (0 : R)), z * algebraMap R S y = x := by
   rcases hz with ⟨p, p_ne_zero, px⟩
   set a := p.leadingCoeff
   have a_ne_zero : a ≠ 0 := mt Polynomial.leadingCoeff_eq_zero.mp p_ne_zero
@@ -404,7 +404,7 @@ if `S` is the integral closure of `R` in an algebraic extension `L` of `R`. -/
 theorem IsIntegralClosure.exists_smul_eq_mul {L : Type*} [Field L] [Algebra R S] [Algebra S L]
     [Algebra R L] [IsScalarTower R S L] [IsIntegralClosure S R L] (h : Algebra.IsAlgebraic R L)
     (inj : Function.Injective (algebraMap R L)) (a : S) {b : S} (hb : b ≠ 0) :
-    ∃ (c : S) (d : _) (_ : d ≠ (0 : R)), d • a = b * c := by
+    ∃ᵉ (c : S) (d ≠ (0 : R)), d • a = b * c := by
   obtain ⟨c, d, d_ne, hx⟩ :=
     exists_integral_multiple (h (algebraMap _ L a / algebraMap _ L b))
       ((injective_iff_map_eq_zero _).mp inj)

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)

@@ -88,9 +88,7 @@ end
 section zero_ne_one
 
 variable {R : Type u} {S : Type*} {A : Type v} [CommRing R]
-
 variable [CommRing S] [Ring A] [Algebra R A] [Algebra R S] [Algebra S A]
-
 variable [IsScalarTower R S A]
 
 /-- An integral element of an algebra is algebraic.-/
@@ -245,7 +243,6 @@ section Ring
 section CommRing
 
 variable [CommRing R] [CommRing S] [Ring A]
-
 variable [Algebra R S] [Algebra S A] [Algebra R A] [IsScalarTower R S A]
 
 /-- If x is algebraic over R, then x is algebraic over S when S is an extension of R,
@@ -270,9 +267,7 @@ end CommRing
 section Field
 
 variable [Field K] [Field L] [Ring A]
-
 variable [Algebra K L] [Algebra L A] [Algebra K A] [IsScalarTower K L A]
-
 variable (L)
 
 /-- If x is algebraic over K, then x is algebraic over L when L is an extension of K -/
@@ -305,7 +300,6 @@ end Ring
 section CommRing
 
 variable [Field K] [Field L] [Ring A]
-
 variable [Algebra K L] [Algebra L A] [Algebra K A] [IsScalarTower K L A]
 
 /-- If L is an algebraic field extension of K and A is an algebraic algebra over L,
@@ -323,7 +317,6 @@ section NoZeroSMulDivisors
 namespace Algebra.IsAlgebraic
 
 variable [CommRing K] [Field L]
-
 variable [Algebra K L] [NoZeroSMulDivisors K L]
 
 theorem algHom_bijective (ha : Algebra.IsAlgebraic K L) (f : L →ₐ[K] L) :
@@ -373,7 +366,6 @@ end NoZeroSMulDivisors
 section Field
 
 variable [Field K] [Field L]
-
 variable [Algebra K L]
 
 theorem AlgHom.bijective [FiniteDimensional K L] (ϕ : L →ₐ[K] L) : Function.Bijective ϕ :=

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.

@@ -21,7 +21,8 @@ a tower of algebraic field extensions is algebraic.
 
 universe u v w
 
-open Classical Polynomial
+open scoped Classical
+open Polynomial
 
 section
 

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

@@ -453,7 +453,7 @@ theorem Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero {x : A} {p : K[X]}
     rw [this]
     exact A.smul_mem (aeval x _).2 _
   have : aeval (x : L) p = 0 := by rw [Subalgebra.aeval_coe, aeval_eq, Subalgebra.coe_zero]
-  -- porting note: this was a long sequence of `rw`.
+  -- Porting note: this was a long sequence of `rw`.
   rw [inv_eq_of_root_of_coeff_zero_ne_zero this coeff_zero_ne, div_eq_inv_mul, Algebra.smul_def]
   simp only [aeval_coe, Submonoid.coe_mul, Subsemiring.coe_toSubmonoid, coe_toSubsemiring,
     coe_algebraMap]
@@ -524,7 +524,7 @@ theorem polynomial_smul_apply' [CommSemiring R'] [Semiring S'] [Algebra R' S'] [
 
 variable [CommSemiring R'] [CommSemiring S'] [CommSemiring T'] [Algebra R' S'] [Algebra S' T']
 
--- porting note: the proofs in this definition used `funext` in term-mode, but I was not able
+-- Porting note: the proofs in this definition used `funext` in term-mode, but I was not able
 -- to get them to work anymore.
 /-- This is not an instance for the same reasons as `Polynomial.hasSMulPi'`. -/
 noncomputable def Polynomial.algebraPi : Algebra R'[X] (S' → T') :=

@@ -193,6 +193,24 @@ theorem Transcendental.pow {r : A} (ht : Transcendental R r) {n : ℕ} (hn : 0 <
     Transcendental R (r ^ n) := fun ht' ↦ ht <| ht'.of_pow hn
 #align transcendental.pow Transcendental.pow
 
+lemma IsAlgebraic.invOf {x : S} [Invertible x] (h : IsAlgebraic R x) : IsAlgebraic R (⅟ x) := by
+  obtain ⟨p, hp, hp'⟩ := h
+  refine ⟨p.reverse, by simpa using hp, ?_⟩
+  rwa [Polynomial.aeval_def, Polynomial.eval₂_reverse_eq_zero_iff, ← Polynomial.aeval_def]
+
+lemma IsAlgebraic.invOf_iff {x : S} [Invertible x] :
+    IsAlgebraic R (⅟ x) ↔ IsAlgebraic R x :=
+  ⟨IsAlgebraic.invOf, IsAlgebraic.invOf⟩
+
+lemma IsAlgebraic.inv_iff {K} [Field K] [Algebra R K] {x : K} :
+    IsAlgebraic R (x⁻¹) ↔ IsAlgebraic R x := by
+  by_cases hx : x = 0
+  · simp [hx]
+  letI := invertibleOfNonzero hx
+  exact IsAlgebraic.invOf_iff (R := R) (x := x)
+
+alias ⟨_, IsAlgebraic.inv⟩ := IsAlgebraic.inv_iff
+
 end zero_ne_one
 
 section Field

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>

@@ -86,7 +86,7 @@ end
 
 section zero_ne_one
 
-variable (R : Type u) {S : Type*} {A : Type v} [CommRing R]
+variable {R : Type u} {S : Type*} {A : Type v} [CommRing R]
 
 variable [CommRing S] [Ring A] [Algebra R A] [Algebra R S] [Algebra S A]
 
@@ -97,7 +97,8 @@ theorem IsIntegral.isAlgebraic [Nontrivial R] {x : A} : IsIntegral R x → IsAlg
   fun ⟨p, hp, hpx⟩ => ⟨p, hp.ne_zero, hpx⟩
 #align is_integral.is_algebraic IsIntegral.isAlgebraic
 
-variable {R}
+theorem Algebra.IsIntegral.isAlgebraic [Nontrivial R] (h : Algebra.IsIntegral R A) :
+    Algebra.IsAlgebraic R A := fun a ↦ (h a).isAlgebraic
 
 theorem isAlgebraic_zero [Nontrivial R] : IsAlgebraic R (0 : A) :=
   ⟨_, X_ne_zero, aeval_X 0⟩
@@ -141,29 +142,43 @@ protected theorem IsAlgebraic.algebraMap {a : S} :
   ⟨f, hf₁, by rw [aeval_algebraMap_apply, hf₂, map_zero]⟩
 #align is_algebraic_algebra_map_of_is_algebraic IsAlgebraic.algebraMap
 
-/-- This is slightly more general than `isAlgebraic_algebraMap_of_isAlgebraic` in that it
+section
+
+variable {B} [Ring B] [Algebra R B]
+
+/-- This is slightly more general than `IsAlgebraic.algebraMap` in that it
   allows noncommutative intermediate rings `A`. -/
-protected theorem IsAlgebraic.algHom {B} [Ring B] [Algebra R B] (f : A →ₐ[R] B) {a : A}
+protected theorem IsAlgebraic.algHom (f : A →ₐ[R] B) {a : A}
     (h : IsAlgebraic R a) : IsAlgebraic R (f a) :=
   let ⟨p, hp, ha⟩ := h
   ⟨p, hp, by rw [aeval_algHom, f.comp_apply, ha, map_zero]⟩
 #align is_algebraic_alg_hom_of_is_algebraic IsAlgebraic.algHom
 
+theorem isAlgebraic_algHom_iff (f : A →ₐ[R] B) (hf : Function.Injective f)
+    {a : A} : IsAlgebraic R (f a) ↔ IsAlgebraic R a :=
+  ⟨fun ⟨p, hp0, hp⟩ ↦ ⟨p, hp0, hf <| by rwa [map_zero, ← f.comp_apply, ← aeval_algHom]⟩,
+    IsAlgebraic.algHom f⟩
+
+theorem Algebra.IsAlgebraic.of_injective (f : A →ₐ[R] B) (hf : Function.Injective f)
+    (h : Algebra.IsAlgebraic R B) : Algebra.IsAlgebraic R A :=
+  fun _ ↦ (isAlgebraic_algHom_iff f hf).mp (h _)
+
 /-- Transfer `Algebra.IsAlgebraic` across an `AlgEquiv`. -/
-theorem AlgEquiv.isAlgebraic {B} [Ring B] [Algebra R B] (e : A ≃ₐ[R] B)
-    (h : Algebra.IsAlgebraic R A) : Algebra.IsAlgebraic R B := fun b => by
-  convert← IsAlgebraic.algHom e.toAlgHom (h _); refine e.apply_symm_apply ?_
+theorem AlgEquiv.isAlgebraic (e : A ≃ₐ[R] B)
+    (h : Algebra.IsAlgebraic R A) : Algebra.IsAlgebraic R B :=
+  h.of_injective e.symm.toAlgHom e.symm.injective
 #align alg_equiv.is_algebraic AlgEquiv.isAlgebraic
 
-theorem AlgEquiv.isAlgebraic_iff {B} [Ring B] [Algebra R B] (e : A ≃ₐ[R] B) :
+theorem AlgEquiv.isAlgebraic_iff (e : A ≃ₐ[R] B) :
     Algebra.IsAlgebraic R A ↔ Algebra.IsAlgebraic R B :=
   ⟨e.isAlgebraic, e.symm.isAlgebraic⟩
 #align alg_equiv.is_algebraic_iff AlgEquiv.isAlgebraic_iff
 
+end
+
 theorem isAlgebraic_algebraMap_iff {a : S} (h : Function.Injective (algebraMap S A)) :
     IsAlgebraic R (algebraMap S A a) ↔ IsAlgebraic R a :=
-  ⟨fun ⟨p, hp0, hp⟩ => ⟨p, hp0, h (by rwa [map_zero, ← aeval_algebraMap_apply])⟩,
-    IsAlgebraic.algebraMap⟩
+  isAlgebraic_algHom_iff (IsScalarTower.toAlgHom R S A) h
 #align is_algebraic_algebra_map_iff isAlgebraic_algebraMap_iff
 
 theorem IsAlgebraic.of_pow {r : A} {n : ℕ} (hn : 0 < n) (ht : IsAlgebraic R (r ^ n)) :
@@ -175,7 +190,7 @@ theorem IsAlgebraic.of_pow {r : A} {n : ℕ} (hn : 0 < n) (ht : IsAlgebraic R (r
 #align is_algebraic_of_pow IsAlgebraic.of_pow
 
 theorem Transcendental.pow {r : A} (ht : Transcendental R r) {n : ℕ} (hn : 0 < n) :
-    Transcendental R (r ^ n) := fun ht' => ht <| IsAlgebraic.of_pow hn ht'
+    Transcendental R (r ^ n) := fun ht' ↦ ht <| ht'.of_pow hn
 #align transcendental.pow Transcendental.pow
 
 end zero_ne_one
@@ -186,7 +201,7 @@ variable {K : Type u} {A : Type v} [Field K] [Ring A] [Algebra K A]
 
 /-- An element of an algebra over a field is algebraic if and only if it is integral.-/
 theorem isAlgebraic_iff_isIntegral {x : A} : IsAlgebraic K x ↔ IsIntegral K x := by
-  refine' ⟨_, IsIntegral.isAlgebraic K⟩
+  refine' ⟨_, IsIntegral.isAlgebraic⟩
   rintro ⟨p, hp, hpx⟩
   refine' ⟨_, monic_mul_leadingCoeff_inv hp, _⟩
   rw [← aeval_def, AlgHom.map_mul, hpx, zero_mul]
@@ -194,14 +209,17 @@ theorem isAlgebraic_iff_isIntegral {x : A} : IsAlgebraic K x ↔ IsIntegral K x
 
 protected theorem Algebra.isAlgebraic_iff_isIntegral :
     Algebra.IsAlgebraic K A ↔ Algebra.IsIntegral K A :=
-  ⟨fun h x => isAlgebraic_iff_isIntegral.mp (h x), fun h x => isAlgebraic_iff_isIntegral.mpr (h x)⟩
+  forall_congr' fun _ ↦ isAlgebraic_iff_isIntegral
 #align algebra.is_algebraic_iff_is_integral Algebra.isAlgebraic_iff_isIntegral
 
+alias ⟨IsAlgebraic.isIntegral, _⟩ := isAlgebraic_iff_isIntegral
+alias ⟨Algebra.IsAlgebraic.isIntegral, _⟩ := Algebra.isAlgebraic_iff_isIntegral
+
 end Field
 
 section
 
-variable {K : Type*} {L : Type*} {R : Type*} {S : Type*} {A : Type*}
+variable {K L R S A : Type*}
 
 section Ring
 
@@ -213,20 +231,20 @@ variable [Algebra R S] [Algebra S A] [Algebra R A] [IsScalarTower R S A]
 
 /-- If x is algebraic over R, then x is algebraic over S when S is an extension of R,
   and the map from `R` to `S` is injective. -/
-theorem IsAlgebraic.of_larger_base_of_injective
+theorem IsAlgebraic.tower_top_of_injective
     (hinj : Function.Injective (algebraMap R S)) {x : A}
     (A_alg : IsAlgebraic R x) : IsAlgebraic S x :=
   let ⟨p, hp₁, hp₂⟩ := A_alg
   ⟨p.map (algebraMap _ _), by
     rwa [Ne.def, ← degree_eq_bot, degree_map_eq_of_injective hinj, degree_eq_bot], by simpa⟩
-#align is_algebraic_of_larger_base_of_injective IsAlgebraic.of_larger_base_of_injective
+#align is_algebraic_of_larger_base_of_injective IsAlgebraic.tower_top_of_injective
 
 /-- If A is an algebraic algebra over R, then A is algebraic over S when S is an extension of R,
   and the map from `R` to `S` is injective. -/
-theorem Algebra.isAlgebraic_of_larger_base_of_injective (hinj : Function.Injective (algebraMap R S))
-    (A_alg : IsAlgebraic R A) : IsAlgebraic S A := fun x =>
-  IsAlgebraic.of_larger_base_of_injective hinj (A_alg x)
-#align algebra.is_algebraic_of_larger_base_of_injective Algebra.isAlgebraic_of_larger_base_of_injective
+theorem Algebra.IsAlgebraic.tower_top_of_injective (hinj : Function.Injective (algebraMap R S))
+    (A_alg : IsAlgebraic R A) : IsAlgebraic S A :=
+  fun x ↦ (A_alg x).tower_top_of_injective hinj
+#align algebra.is_algebraic_of_larger_base_of_injective Algebra.IsAlgebraic.tower_top_of_injective
 
 end CommRing
 
@@ -239,27 +257,27 @@ variable [Algebra K L] [Algebra L A] [Algebra K A] [IsScalarTower K L A]
 variable (L)
 
 /-- If x is algebraic over K, then x is algebraic over L when L is an extension of K -/
-theorem IsAlgebraic.of_larger_base {x : A} (A_alg : IsAlgebraic K x) :
+theorem IsAlgebraic.tower_top {x : A} (A_alg : IsAlgebraic K x) :
     IsAlgebraic L x :=
-  IsAlgebraic.of_larger_base_of_injective (algebraMap K L).injective A_alg
-#align is_algebraic_of_larger_base IsAlgebraic.of_larger_base
+  A_alg.tower_top_of_injective (algebraMap K L).injective
+#align is_algebraic_of_larger_base IsAlgebraic.tower_top
 
 /-- If A is an algebraic algebra over K, then A is algebraic over L when L is an extension of K -/
-theorem Algebra.isAlgebraic_of_larger_base (A_alg : IsAlgebraic K A) : IsAlgebraic L A :=
-  isAlgebraic_of_larger_base_of_injective (algebraMap K L).injective A_alg
-#align algebra.is_algebraic_of_larger_base Algebra.isAlgebraic_of_larger_base
+theorem Algebra.IsAlgebraic.tower_top (A_alg : IsAlgebraic K A) : IsAlgebraic L A :=
+  A_alg.tower_top_of_injective (algebraMap K L).injective
+#align algebra.is_algebraic_of_larger_base Algebra.IsAlgebraic.tower_top
 
 variable (K)
 
 theorem IsAlgebraic.of_finite (e : A) [FiniteDimensional K A] : IsAlgebraic K e :=
-  isAlgebraic_iff_isIntegral.mpr (IsIntegral.of_finite K e)
+  (IsIntegral.of_finite K e).isAlgebraic
 
 variable (A)
 
 /-- A field extension is algebraic if it is finite. -/
-theorem Algebra.isAlgebraic_of_finite [FiniteDimensional K A] : IsAlgebraic K A :=
-  Algebra.isAlgebraic_iff_isIntegral.mpr (isIntegral_of_finite K A)
-#align algebra.is_algebraic_of_finite Algebra.isAlgebraic_of_finite
+theorem Algebra.IsAlgebraic.of_finite [FiniteDimensional K A] : IsAlgebraic K A :=
+  (IsIntegral.of_finite K A).isAlgebraic
+#align algebra.is_algebraic_of_finite Algebra.IsAlgebraic.of_finite
 
 end Field
 
@@ -267,27 +285,29 @@ end Ring
 
 section CommRing
 
-variable [Field K] [Field L] [CommRing A]
+variable [Field K] [Field L] [Ring A]
 
 variable [Algebra K L] [Algebra L A] [Algebra K A] [IsScalarTower K L A]
 
 /-- If L is an algebraic field extension of K and A is an algebraic algebra over L,
 then A is algebraic over K. -/
-theorem Algebra.isAlgebraic_trans (L_alg : IsAlgebraic K L) (A_alg : IsAlgebraic L A) :
+protected theorem Algebra.IsAlgebraic.trans (L_alg : IsAlgebraic K L) (A_alg : IsAlgebraic L A) :
     IsAlgebraic K A := by
-  simp only [IsAlgebraic, isAlgebraic_iff_isIntegral] at L_alg A_alg ⊢
-  exact isIntegral_trans L_alg A_alg
-#align algebra.is_algebraic_trans Algebra.isAlgebraic_trans
+  rw [Algebra.isAlgebraic_iff_isIntegral] at L_alg A_alg ⊢
+  exact L_alg.trans A_alg
+#align algebra.is_algebraic_trans Algebra.IsAlgebraic.trans
 
 end CommRing
 
 section NoZeroSMulDivisors
 
+namespace Algebra.IsAlgebraic
+
 variable [CommRing K] [Field L]
 
 variable [Algebra K L] [NoZeroSMulDivisors K L]
 
-theorem Algebra.IsAlgebraic.algHom_bijective (ha : Algebra.IsAlgebraic K L) (f : L →ₐ[K] L) :
+theorem algHom_bijective (ha : Algebra.IsAlgebraic K L) (f : L →ₐ[K] L) :
     Function.Bijective f := by
   refine' ⟨f.injective, fun b ↦ _⟩
   obtain ⟨p, hp, he⟩ := ha b
@@ -298,17 +318,17 @@ theorem Algebra.IsAlgebraic.algHom_bijective (ha : Algebra.IsAlgebraic K L) (f :
   exact ⟨a, Subtype.ext_iff.1 ha⟩
 #align algebra.is_algebraic.alg_hom_bijective Algebra.IsAlgebraic.algHom_bijective
 
-theorem Algebra.IsAlgebraic.algHom_bijective₂ [Field R] [Algebra K R]
+theorem algHom_bijective₂ [Field R] [Algebra K R]
     (ha : Algebra.IsAlgebraic K L) (f : L →ₐ[K] R) (g : R →ₐ[K] L) :
     Function.Bijective f ∧ Function.Bijective g :=
   (g.injective.bijective₂_of_surjective f.injective (ha.algHom_bijective <| g.comp f).2).symm
 
-theorem Algebra.IsAlgebraic.bijective_of_isScalarTower (ha : Algebra.IsAlgebraic K L)
+theorem bijective_of_isScalarTower (ha : Algebra.IsAlgebraic K L)
     [Field R] [Algebra K R] [Algebra L R] [IsScalarTower K L R] (f : R →ₐ[K] L) :
     Function.Bijective f :=
   (ha.algHom_bijective₂ (IsScalarTower.toAlgHom K L R) f).2
 
-theorem Algebra.IsAlgebraic.bijective_of_isScalarTower' [Field R] [Algebra K R]
+theorem bijective_of_isScalarTower' [Field R] [Algebra K R]
     [NoZeroSMulDivisors K R]
     (ha : Algebra.IsAlgebraic K R) [Algebra L R] [IsScalarTower K L R] (f : R →ₐ[K] L) :
     Function.Bijective f :=
@@ -318,19 +338,17 @@ variable (K L)
 
 /-- Bijection between algebra equivalences and algebra homomorphisms -/
 @[simps]
-noncomputable def Algebra.IsAlgebraic.algEquivEquivAlgHom (ha : Algebra.IsAlgebraic K L) :
+noncomputable def algEquivEquivAlgHom (ha : Algebra.IsAlgebraic K L) :
     (L ≃ₐ[K] L) ≃* (L →ₐ[K] L) where
   toFun ϕ := ϕ.toAlgHom
   invFun ϕ := AlgEquiv.ofBijective ϕ (ha.algHom_bijective ϕ)
-  left_inv _ := by
-    ext
-    rfl
-  right_inv _ := by
-    ext
-    rfl
+  left_inv _ := by ext; rfl
+  right_inv _ := by ext; rfl
   map_mul' _ _ := rfl
 #align algebra.is_algebraic.alg_equiv_equiv_alg_hom Algebra.IsAlgebraic.algEquivEquivAlgHom
 
+end Algebra.IsAlgebraic
+
 end NoZeroSMulDivisors
 
 section Field
@@ -340,7 +358,7 @@ variable [Field K] [Field L]
 variable [Algebra K L]
 
 theorem AlgHom.bijective [FiniteDimensional K L] (ϕ : L →ₐ[K] L) : Function.Bijective ϕ :=
-  (Algebra.isAlgebraic_of_finite K L).algHom_bijective ϕ
+  (Algebra.IsAlgebraic.of_finite K L).algHom_bijective ϕ
 #align alg_hom.bijective AlgHom.bijective
 
 variable (K L)
@@ -349,7 +367,7 @@ variable (K L)
 @[reducible]
 noncomputable def algEquivEquivAlgHom [FiniteDimensional K L] :
     (L ≃ₐ[K] L) ≃* (L →ₐ[K] L) :=
-  (Algebra.isAlgebraic_of_finite K L).algEquivEquivAlgHom K L
+  (Algebra.IsAlgebraic.of_finite K L).algEquivEquivAlgHom K L
 #align alg_equiv_equiv_alg_hom algEquivEquivAlgHom
 
 end Field

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 |

@@ -136,23 +136,23 @@ theorem isAlgebraic_of_mem_rootSet {R : Type u} {A : Type v} [Field R] [Field A]
 
 open IsScalarTower
 
-theorem isAlgebraic_algebraMap_of_isAlgebraic {a : S} :
+protected theorem IsAlgebraic.algebraMap {a : S} :
     IsAlgebraic R a → IsAlgebraic R (algebraMap S A a) := fun ⟨f, hf₁, hf₂⟩ =>
   ⟨f, hf₁, by rw [aeval_algebraMap_apply, hf₂, map_zero]⟩
-#align is_algebraic_algebra_map_of_is_algebraic isAlgebraic_algebraMap_of_isAlgebraic
+#align is_algebraic_algebra_map_of_is_algebraic IsAlgebraic.algebraMap
 
 /-- This is slightly more general than `isAlgebraic_algebraMap_of_isAlgebraic` in that it
   allows noncommutative intermediate rings `A`. -/
-theorem isAlgebraic_algHom_of_isAlgebraic {B} [Ring B] [Algebra R B] (f : A →ₐ[R] B) {a : A}
+protected theorem IsAlgebraic.algHom {B} [Ring B] [Algebra R B] (f : A →ₐ[R] B) {a : A}
     (h : IsAlgebraic R a) : IsAlgebraic R (f a) :=
   let ⟨p, hp, ha⟩ := h
   ⟨p, hp, by rw [aeval_algHom, f.comp_apply, ha, map_zero]⟩
-#align is_algebraic_alg_hom_of_is_algebraic isAlgebraic_algHom_of_isAlgebraic
+#align is_algebraic_alg_hom_of_is_algebraic IsAlgebraic.algHom
 
 /-- Transfer `Algebra.IsAlgebraic` across an `AlgEquiv`. -/
 theorem AlgEquiv.isAlgebraic {B} [Ring B] [Algebra R B] (e : A ≃ₐ[R] B)
     (h : Algebra.IsAlgebraic R A) : Algebra.IsAlgebraic R B := fun b => by
-  convert← isAlgebraic_algHom_of_isAlgebraic e.toAlgHom (h _); refine e.apply_symm_apply ?_
+  convert← IsAlgebraic.algHom e.toAlgHom (h _); refine e.apply_symm_apply ?_
 #align alg_equiv.is_algebraic AlgEquiv.isAlgebraic
 
 theorem AlgEquiv.isAlgebraic_iff {B} [Ring B] [Algebra R B] (e : A ≃ₐ[R] B) :
@@ -163,19 +163,19 @@ theorem AlgEquiv.isAlgebraic_iff {B} [Ring B] [Algebra R B] (e : A ≃ₐ[R] B)
 theorem isAlgebraic_algebraMap_iff {a : S} (h : Function.Injective (algebraMap S A)) :
     IsAlgebraic R (algebraMap S A a) ↔ IsAlgebraic R a :=
   ⟨fun ⟨p, hp0, hp⟩ => ⟨p, hp0, h (by rwa [map_zero, ← aeval_algebraMap_apply])⟩,
-    isAlgebraic_algebraMap_of_isAlgebraic⟩
+    IsAlgebraic.algebraMap⟩
 #align is_algebraic_algebra_map_iff isAlgebraic_algebraMap_iff
 
-theorem isAlgebraic_of_pow {r : A} {n : ℕ} (hn : 0 < n) (ht : IsAlgebraic R (r ^ n)) :
+theorem IsAlgebraic.of_pow {r : A} {n : ℕ} (hn : 0 < n) (ht : IsAlgebraic R (r ^ n)) :
     IsAlgebraic R r := by
   obtain ⟨p, p_nonzero, hp⟩ := ht
   refine ⟨Polynomial.expand _ n p, ?_, ?_⟩
   · rwa [Polynomial.expand_ne_zero hn]
   · rwa [Polynomial.expand_aeval n p r]
-#align is_algebraic_of_pow isAlgebraic_of_pow
+#align is_algebraic_of_pow IsAlgebraic.of_pow
 
 theorem Transcendental.pow {r : A} (ht : Transcendental R r) {n : ℕ} (hn : 0 < n) :
-    Transcendental R (r ^ n) := fun ht' => ht <| isAlgebraic_of_pow hn ht'
+    Transcendental R (r ^ n) := fun ht' => ht <| IsAlgebraic.of_pow hn ht'
 #align transcendental.pow Transcendental.pow
 
 end zero_ne_one
@@ -213,19 +213,19 @@ variable [Algebra R S] [Algebra S A] [Algebra R A] [IsScalarTower R S A]
 
 /-- If x is algebraic over R, then x is algebraic over S when S is an extension of R,
   and the map from `R` to `S` is injective. -/
-theorem isAlgebraic_of_larger_base_of_injective
+theorem IsAlgebraic.of_larger_base_of_injective
     (hinj : Function.Injective (algebraMap R S)) {x : A}
     (A_alg : IsAlgebraic R x) : IsAlgebraic S x :=
   let ⟨p, hp₁, hp₂⟩ := A_alg
   ⟨p.map (algebraMap _ _), by
     rwa [Ne.def, ← degree_eq_bot, degree_map_eq_of_injective hinj, degree_eq_bot], by simpa⟩
-#align is_algebraic_of_larger_base_of_injective isAlgebraic_of_larger_base_of_injective
+#align is_algebraic_of_larger_base_of_injective IsAlgebraic.of_larger_base_of_injective
 
 /-- If A is an algebraic algebra over R, then A is algebraic over S when S is an extension of R,
   and the map from `R` to `S` is injective. -/
 theorem Algebra.isAlgebraic_of_larger_base_of_injective (hinj : Function.Injective (algebraMap R S))
     (A_alg : IsAlgebraic R A) : IsAlgebraic S A := fun x =>
-  _root_.isAlgebraic_of_larger_base_of_injective hinj (A_alg x)
+  IsAlgebraic.of_larger_base_of_injective hinj (A_alg x)
 #align algebra.is_algebraic_of_larger_base_of_injective Algebra.isAlgebraic_of_larger_base_of_injective
 
 end CommRing
@@ -239,10 +239,10 @@ variable [Algebra K L] [Algebra L A] [Algebra K A] [IsScalarTower K L A]
 variable (L)
 
 /-- If x is algebraic over K, then x is algebraic over L when L is an extension of K -/
-theorem isAlgebraic_of_larger_base {x : A} (A_alg : IsAlgebraic K x) :
+theorem IsAlgebraic.of_larger_base {x : A} (A_alg : IsAlgebraic K x) :
     IsAlgebraic L x :=
-  isAlgebraic_of_larger_base_of_injective (algebraMap K L).injective A_alg
-#align is_algebraic_of_larger_base isAlgebraic_of_larger_base
+  IsAlgebraic.of_larger_base_of_injective (algebraMap K L).injective A_alg
+#align is_algebraic_of_larger_base IsAlgebraic.of_larger_base
 
 /-- If A is an algebraic algebra over K, then A is algebraic over L when L is an extension of K -/
 theorem Algebra.isAlgebraic_of_larger_base (A_alg : IsAlgebraic K A) : IsAlgebraic L A :=
@@ -251,8 +251,8 @@ theorem Algebra.isAlgebraic_of_larger_base (A_alg : IsAlgebraic K A) : IsAlgebra
 
 variable (K)
 
-theorem isAlgebraic_of_finite (e : A) [FiniteDimensional K A] : IsAlgebraic K e :=
-  isAlgebraic_iff_isIntegral.mpr (isIntegral_of_finite K e)
+theorem IsAlgebraic.of_finite (e : A) [FiniteDimensional K A] : IsAlgebraic K e :=
+  isAlgebraic_iff_isIntegral.mpr (IsIntegral.of_finite K e)
 
 variable (A)
 

• IsSepClosed.lift is a map from a separable extension L of K, into any separably closed extension M of K.

• IsSepClosure.equiv is a proof that any two separable closures of the same field are isomorphic.

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

@@ -281,11 +281,11 @@ theorem Algebra.isAlgebraic_trans (L_alg : IsAlgebraic K L) (A_alg : IsAlgebraic
 
 end CommRing
 
-section Field
+section NoZeroSMulDivisors
 
-variable [Field K] [Field L]
+variable [CommRing K] [Field L]
 
-variable [Algebra K L]
+variable [Algebra K L] [NoZeroSMulDivisors K L]
 
 theorem Algebra.IsAlgebraic.algHom_bijective (ha : Algebra.IsAlgebraic K L) (f : L →ₐ[K] L) :
     Function.Bijective f := by
@@ -309,14 +309,11 @@ theorem Algebra.IsAlgebraic.bijective_of_isScalarTower (ha : Algebra.IsAlgebraic
   (ha.algHom_bijective₂ (IsScalarTower.toAlgHom K L R) f).2
 
 theorem Algebra.IsAlgebraic.bijective_of_isScalarTower' [Field R] [Algebra K R]
+    [NoZeroSMulDivisors K R]
     (ha : Algebra.IsAlgebraic K R) [Algebra L R] [IsScalarTower K L R] (f : R →ₐ[K] L) :
     Function.Bijective f :=
   (ha.algHom_bijective₂ f (IsScalarTower.toAlgHom K L R)).1
 
-theorem AlgHom.bijective [FiniteDimensional K L] (ϕ : L →ₐ[K] L) : Function.Bijective ϕ :=
-  (Algebra.isAlgebraic_of_finite K L).algHom_bijective ϕ
-#align alg_hom.bijective AlgHom.bijective
-
 variable (K L)
 
 /-- Bijection between algebra equivalences and algebra homomorphisms -/
@@ -334,6 +331,20 @@ noncomputable def Algebra.IsAlgebraic.algEquivEquivAlgHom (ha : Algebra.IsAlgebr
   map_mul' _ _ := rfl
 #align algebra.is_algebraic.alg_equiv_equiv_alg_hom Algebra.IsAlgebraic.algEquivEquivAlgHom
 
+end NoZeroSMulDivisors
+
+section Field
+
+variable [Field K] [Field L]
+
+variable [Algebra K L]
+
+theorem AlgHom.bijective [FiniteDimensional K L] (ϕ : L →ₐ[K] L) : Function.Bijective ϕ :=
+  (Algebra.isAlgebraic_of_finite K L).algHom_bijective ϕ
+#align alg_hom.bijective AlgHom.bijective
+
+variable (K L)
+
 /-- Bijection between algebra equivalences and algebra homomorphisms -/
 @[reducible]
 noncomputable def algEquivEquivAlgHom [FiniteDimensional K L] :

Also golfs Normal.of_algEquiv and Algebra.IsIntegral.of_finite and refactors Algebra.IsAlgebraic.bijective_of_isScalarTower.

@@ -298,17 +298,20 @@ theorem Algebra.IsAlgebraic.algHom_bijective (ha : Algebra.IsAlgebraic K L) (f :
   exact ⟨a, Subtype.ext_iff.1 ha⟩
 #align algebra.is_algebraic.alg_hom_bijective Algebra.IsAlgebraic.algHom_bijective
 
+theorem Algebra.IsAlgebraic.algHom_bijective₂ [Field R] [Algebra K R]
+    (ha : Algebra.IsAlgebraic K L) (f : L →ₐ[K] R) (g : R →ₐ[K] L) :
+    Function.Bijective f ∧ Function.Bijective g :=
+  (g.injective.bijective₂_of_surjective f.injective (ha.algHom_bijective <| g.comp f).2).symm
+
 theorem Algebra.IsAlgebraic.bijective_of_isScalarTower (ha : Algebra.IsAlgebraic K L)
     [Field R] [Algebra K R] [Algebra L R] [IsScalarTower K L R] (f : R →ₐ[K] L) :
     Function.Bijective f :=
-  ⟨f.injective, Function.Surjective.of_comp <|
-    (ha.algHom_bijective <| f.comp <| IsScalarTower.toAlgHom K L R).2⟩
+  (ha.algHom_bijective₂ (IsScalarTower.toAlgHom K L R) f).2
 
 theorem Algebra.IsAlgebraic.bijective_of_isScalarTower' [Field R] [Algebra K R]
     (ha : Algebra.IsAlgebraic K R) [Algebra L R] [IsScalarTower K L R] (f : R →ₐ[K] L) :
     Function.Bijective f :=
-  ⟨f.injective, Function.Surjective.of_comp_left
-    (ha.algHom_bijective <| (IsScalarTower.toAlgHom K L R).comp f).2 (RingHom.injective _)⟩
+  (ha.algHom_bijective₂ f (IsScalarTower.toAlgHom K L R)).1
 
 theorem AlgHom.bijective [FiniteDimensional K L] (ϕ : L →ₐ[K] L) : Function.Bijective ϕ :=
   (Algebra.isAlgebraic_of_finite K L).algHom_bijective ϕ

Add Normal.minpoly_eq_iff_mem_orbit: addresses https://github.com/leanprover-community/mathlib4/pull/6718/files#r1328899532

Also generalize AlgHom.normal_bijective to Algebra.IsAlgebraic.bijective_of_isScalarTower' and golf the proof using a set-theoretic lemma Surjective.of_comp_left (slow to build, awaiting CI).

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

@@ -289,16 +289,27 @@ variable [Algebra K L]
 
 theorem Algebra.IsAlgebraic.algHom_bijective (ha : Algebra.IsAlgebraic K L) (f : L →ₐ[K] L) :
     Function.Bijective f := by
-  refine' ⟨f.toRingHom.injective, fun b => _⟩
+  refine' ⟨f.injective, fun b ↦ _⟩
   obtain ⟨p, hp, he⟩ := ha b
-  let f' : p.rootSet L → p.rootSet L := (rootSet_maps_to' (fun x => x) f).restrict f _ _
-  have : Function.Surjective f' :=
-    Finite.injective_iff_surjective.1 fun _ _ h =>
-      Subtype.eq <| f.toRingHom.injective <| Subtype.ext_iff.1 h
+  let f' : p.rootSet L → p.rootSet L := (rootSet_maps_to' (fun x ↦ x) f).restrict f _ _
+  have : f'.Surjective := Finite.injective_iff_surjective.1
+    fun _ _ h ↦ Subtype.eq <| f.injective <| Subtype.ext_iff.1 h
   obtain ⟨a, ha⟩ := this ⟨b, mem_rootSet.2 ⟨hp, he⟩⟩
   exact ⟨a, Subtype.ext_iff.1 ha⟩
 #align algebra.is_algebraic.alg_hom_bijective Algebra.IsAlgebraic.algHom_bijective
 
+theorem Algebra.IsAlgebraic.bijective_of_isScalarTower (ha : Algebra.IsAlgebraic K L)
+    [Field R] [Algebra K R] [Algebra L R] [IsScalarTower K L R] (f : R →ₐ[K] L) :
+    Function.Bijective f :=
+  ⟨f.injective, Function.Surjective.of_comp <|
+    (ha.algHom_bijective <| f.comp <| IsScalarTower.toAlgHom K L R).2⟩
+
+theorem Algebra.IsAlgebraic.bijective_of_isScalarTower' [Field R] [Algebra K R]
+    (ha : Algebra.IsAlgebraic K R) [Algebra L R] [IsScalarTower K L R] (f : R →ₐ[K] L) :
+    Function.Bijective f :=
+  ⟨f.injective, Function.Surjective.of_comp_left
+    (ha.algHom_bijective <| (IsScalarTower.toAlgHom K L R).comp f).2 (RingHom.injective _)⟩
+
 theorem AlgHom.bijective [FiniteDimensional K L] (ϕ : L →ₐ[K] L) : Function.Bijective ϕ :=
   (Algebra.isAlgebraic_of_finite K L).algHom_bijective ϕ
 #align alg_hom.bijective AlgHom.bijective

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).

@@ -189,7 +189,7 @@ theorem isAlgebraic_iff_isIntegral {x : A} : IsAlgebraic K x ↔ IsIntegral K x
   refine' ⟨_, IsIntegral.isAlgebraic K⟩
   rintro ⟨p, hp, hpx⟩
   refine' ⟨_, monic_mul_leadingCoeff_inv hp, _⟩
-  rw [← aeval_def, AlgHom.map_mul, hpx, MulZeroClass.zero_mul]
+  rw [← aeval_def, AlgHom.map_mul, hpx, zero_mul]
 #align is_algebraic_iff_is_integral isAlgebraic_iff_isIntegral
 
 protected theorem Algebra.isAlgebraic_iff_isIntegral :
@@ -383,7 +383,7 @@ theorem inv_eq_of_root_of_coeff_zero_ne_zero {x : L} {p : K[X]} (aeval_eq : aeva
   rw [RingHom.map_zero]
   convert aeval_eq
   conv_rhs => rw [← divX_mul_X_add p]
-  rw [AlgHom.map_add, AlgHom.map_mul, h, MulZeroClass.zero_mul, zero_add, aeval_C]
+  rw [AlgHom.map_add, AlgHom.map_mul, h, zero_mul, zero_add, aeval_C]
 #align inv_eq_of_root_of_coeff_zero_ne_zero inv_eq_of_root_of_coeff_zero_ne_zero
 
 theorem Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero {x : A} {p : K[X]}

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

This has nice performance benefits.

@@ -86,7 +86,7 @@ end
 
 section zero_ne_one
 
-variable (R : Type u) {S : Type _} {A : Type v} [CommRing R]
+variable (R : Type u) {S : Type*} {A : Type v} [CommRing R]
 
 variable [CommRing S] [Ring A] [Algebra R A] [Algebra R S] [Algebra S A]
 
@@ -201,7 +201,7 @@ end Field
 
 section
 
-variable {K : Type _} {L : Type _} {R : Type _} {S : Type _} {A : Type _}
+variable {K : Type*} {L : Type*} {R : Type*} {S : Type*} {A : Type*}
 
 section Ring
 
@@ -331,7 +331,7 @@ end Field
 
 end
 
-variable {R S : Type _} [CommRing R] [IsDomain R] [CommRing S]
+variable {R S : Type*} [CommRing R] [IsDomain R] [CommRing S]
 
 theorem exists_integral_multiple [Algebra R S] {z : S} (hz : IsAlgebraic R z)
     (inj : ∀ x, algebraMap R S x = 0 → x = 0) :
@@ -347,7 +347,7 @@ theorem exists_integral_multiple [Algebra R S] {z : S} (hz : IsAlgebraic R z)
 
 /-- A fraction `(a : S) / (b : S)` can be reduced to `(c : S) / (d : R)`,
 if `S` is the integral closure of `R` in an algebraic extension `L` of `R`. -/
-theorem IsIntegralClosure.exists_smul_eq_mul {L : Type _} [Field L] [Algebra R S] [Algebra S L]
+theorem IsIntegralClosure.exists_smul_eq_mul {L : Type*} [Field L] [Algebra R S] [Algebra S L]
     [Algebra R L] [IsScalarTower R S L] [IsIntegralClosure S R L] (h : Algebra.IsAlgebraic R L)
     (inj : Function.Injective (algebraMap R L)) (a : S) {b : S} (hb : b ≠ 0) :
     ∃ (c : S) (d : _) (_ : d ≠ (0 : R)), d • a = b * c := by
@@ -364,7 +364,7 @@ theorem IsIntegralClosure.exists_smul_eq_mul {L : Type _} [Field L] [Algebra R S
 
 section Field
 
-variable {K L : Type _} [Field K] [Field L] [Algebra K L] (A : Subalgebra K L)
+variable {K L : Type*} [Field K] [Field L] [Algebra K L] (A : Subalgebra K L)
 
 theorem inv_eq_of_aeval_divX_ne_zero {x : L} {p : K[X]} (aeval_ne : aeval x (divX p) ≠ 0) :
     x⁻¹ = aeval x (divX p) / (aeval x p - algebraMap _ _ (p.coeff 0)) := by

A similar file ScaleRoots is also in RingTheory/Polynomial.

@@ -5,7 +5,7 @@ Authors: Johan Commelin
 -/
 import Mathlib.LinearAlgebra.FiniteDimensional
 import Mathlib.RingTheory.IntegralClosure
-import Mathlib.Data.Polynomial.IntegralNormalization
+import Mathlib.RingTheory.Polynomial.IntegralNormalization
 
 #align_import ring_theory.algebraic from "leanprover-community/mathlib"@"2196ab363eb097c008d4497125e0dde23fb36db2"
 

Also

• fix the names of minpoly.natDegree_le and minpoly.degree_le
• rename minpoly.ne_zero_of_finite_field_extension to minpoly.ne_zero_of_finite
• reduce typeclass assumptions of some lemmas in RingTheory/Algebraic
• add two lemmas isIntegral_of_finite and isAlgebraic_of_finite
• move Algebra.isIntegral_of_finite to RingTheory/IntegralClosure

@@ -199,31 +199,23 @@ protected theorem Algebra.isAlgebraic_iff_isIntegral :
 
 end Field
 
-namespace Algebra
+section
 
 variable {K : Type _} {L : Type _} {R : Type _} {S : Type _} {A : Type _}
 
-variable [Field K] [Field L] [CommRing R] [CommRing S] [CommRing A]
+section Ring
 
-variable [Algebra K L] [Algebra L A] [Algebra K A] [IsScalarTower K L A]
+section CommRing
 
-variable [Algebra R S] [Algebra S A] [Algebra R A] [IsScalarTower R S A]
+variable [CommRing R] [CommRing S] [Ring A]
 
-/-- If L is an algebraic field extension of K and A is an algebraic algebra over L,
-then A is algebraic over K. -/
-theorem isAlgebraic_trans (L_alg : IsAlgebraic K L) (A_alg : IsAlgebraic L A) :
-    IsAlgebraic K A := by
-  simp only [IsAlgebraic, isAlgebraic_iff_isIntegral] at L_alg A_alg ⊢
-  exact isIntegral_trans L_alg A_alg
-#align algebra.is_algebraic_trans Algebra.isAlgebraic_trans
-
-variable (K L)
+variable [Algebra R S] [Algebra S A] [Algebra R A] [IsScalarTower R S A]
 
 /-- If x is algebraic over R, then x is algebraic over S when S is an extension of R,
   and the map from `R` to `S` is injective. -/
-theorem _root_.isAlgebraic_of_larger_base_of_injective
+theorem isAlgebraic_of_larger_base_of_injective
     (hinj : Function.Injective (algebraMap R S)) {x : A}
-    (A_alg : _root_.IsAlgebraic R x) : _root_.IsAlgebraic S x :=
+    (A_alg : IsAlgebraic R x) : IsAlgebraic S x :=
   let ⟨p, hp₁, hp₂⟩ := A_alg
   ⟨p.map (algebraMap _ _), by
     rwa [Ne.def, ← degree_eq_bot, degree_map_eq_of_injective hinj, degree_eq_bot], by simpa⟩
@@ -231,35 +223,71 @@ theorem _root_.isAlgebraic_of_larger_base_of_injective
 
 /-- If A is an algebraic algebra over R, then A is algebraic over S when S is an extension of R,
   and the map from `R` to `S` is injective. -/
-theorem isAlgebraic_of_larger_base_of_injective (hinj : Function.Injective (algebraMap R S))
+theorem Algebra.isAlgebraic_of_larger_base_of_injective (hinj : Function.Injective (algebraMap R S))
     (A_alg : IsAlgebraic R A) : IsAlgebraic S A := fun x =>
   _root_.isAlgebraic_of_larger_base_of_injective hinj (A_alg x)
 #align algebra.is_algebraic_of_larger_base_of_injective Algebra.isAlgebraic_of_larger_base_of_injective
 
+end CommRing
+
+section Field
+
+variable [Field K] [Field L] [Ring A]
+
+variable [Algebra K L] [Algebra L A] [Algebra K A] [IsScalarTower K L A]
+
+variable (L)
+
 /-- If x is algebraic over K, then x is algebraic over L when L is an extension of K -/
-theorem _root_.isAlgebraic_of_larger_base {x : A} (A_alg : _root_.IsAlgebraic K x) :
-    _root_.IsAlgebraic L x :=
-  _root_.isAlgebraic_of_larger_base_of_injective (algebraMap K L).injective A_alg
+theorem isAlgebraic_of_larger_base {x : A} (A_alg : IsAlgebraic K x) :
+    IsAlgebraic L x :=
+  isAlgebraic_of_larger_base_of_injective (algebraMap K L).injective A_alg
 #align is_algebraic_of_larger_base isAlgebraic_of_larger_base
 
 /-- If A is an algebraic algebra over K, then A is algebraic over L when L is an extension of K -/
-theorem isAlgebraic_of_larger_base (A_alg : IsAlgebraic K A) : IsAlgebraic L A :=
+theorem Algebra.isAlgebraic_of_larger_base (A_alg : IsAlgebraic K A) : IsAlgebraic L A :=
   isAlgebraic_of_larger_base_of_injective (algebraMap K L).injective A_alg
 #align algebra.is_algebraic_of_larger_base Algebra.isAlgebraic_of_larger_base
 
-/-- A field extension is integral if it is finite. -/
-theorem isIntegral_of_finite [FiniteDimensional K L] : Algebra.IsIntegral K L := fun x =>
-  isIntegral_of_submodule_noetherian ⊤ (IsNoetherian.iff_fg.2 inferInstance) x Algebra.mem_top
-#align algebra.is_integral_of_finite Algebra.isIntegral_of_finite
+variable (K)
+
+theorem isAlgebraic_of_finite (e : A) [FiniteDimensional K A] : IsAlgebraic K e :=
+  isAlgebraic_iff_isIntegral.mpr (isIntegral_of_finite K e)
+
+variable (A)
 
 /-- A field extension is algebraic if it is finite. -/
-theorem isAlgebraic_of_finite [FiniteDimensional K L] : IsAlgebraic K L :=
-  Algebra.isAlgebraic_iff_isIntegral.mpr (isIntegral_of_finite K L)
+theorem Algebra.isAlgebraic_of_finite [FiniteDimensional K A] : IsAlgebraic K A :=
+  Algebra.isAlgebraic_iff_isIntegral.mpr (isIntegral_of_finite K A)
 #align algebra.is_algebraic_of_finite Algebra.isAlgebraic_of_finite
 
-variable {K L}
+end Field
+
+end Ring
+
+section CommRing
+
+variable [Field K] [Field L] [CommRing A]
+
+variable [Algebra K L] [Algebra L A] [Algebra K A] [IsScalarTower K L A]
 
-theorem IsAlgebraic.algHom_bijective (ha : Algebra.IsAlgebraic K L) (f : L →ₐ[K] L) :
+/-- If L is an algebraic field extension of K and A is an algebraic algebra over L,
+then A is algebraic over K. -/
+theorem Algebra.isAlgebraic_trans (L_alg : IsAlgebraic K L) (A_alg : IsAlgebraic L A) :
+    IsAlgebraic K A := by
+  simp only [IsAlgebraic, isAlgebraic_iff_isIntegral] at L_alg A_alg ⊢
+  exact isIntegral_trans L_alg A_alg
+#align algebra.is_algebraic_trans Algebra.isAlgebraic_trans
+
+end CommRing
+
+section Field
+
+variable [Field K] [Field L]
+
+variable [Algebra K L]
+
+theorem Algebra.IsAlgebraic.algHom_bijective (ha : Algebra.IsAlgebraic K L) (f : L →ₐ[K] L) :
     Function.Bijective f := by
   refine' ⟨f.toRingHom.injective, fun b => _⟩
   obtain ⟨p, hp, he⟩ := ha b
@@ -271,7 +299,7 @@ theorem IsAlgebraic.algHom_bijective (ha : Algebra.IsAlgebraic K L) (f : L →
   exact ⟨a, Subtype.ext_iff.1 ha⟩
 #align algebra.is_algebraic.alg_hom_bijective Algebra.IsAlgebraic.algHom_bijective
 
-theorem _root_.AlgHom.bijective [FiniteDimensional K L] (ϕ : L →ₐ[K] L) : Function.Bijective ϕ :=
+theorem AlgHom.bijective [FiniteDimensional K L] (ϕ : L →ₐ[K] L) : Function.Bijective ϕ :=
   (Algebra.isAlgebraic_of_finite K L).algHom_bijective ϕ
 #align alg_hom.bijective AlgHom.bijective
 
@@ -279,7 +307,7 @@ variable (K L)
 
 /-- Bijection between algebra equivalences and algebra homomorphisms -/
 @[simps]
-noncomputable def IsAlgebraic.algEquivEquivAlgHom (ha : Algebra.IsAlgebraic K L) :
+noncomputable def Algebra.IsAlgebraic.algEquivEquivAlgHom (ha : Algebra.IsAlgebraic K L) :
     (L ≃ₐ[K] L) ≃* (L →ₐ[K] L) where
   toFun ϕ := ϕ.toAlgHom
   invFun ϕ := AlgEquiv.ofBijective ϕ (ha.algHom_bijective ϕ)
@@ -294,12 +322,14 @@ noncomputable def IsAlgebraic.algEquivEquivAlgHom (ha : Algebra.IsAlgebraic K L)
 
 /-- Bijection between algebra equivalences and algebra homomorphisms -/
 @[reducible]
-noncomputable def _root_.algEquivEquivAlgHom [FiniteDimensional K L] :
+noncomputable def algEquivEquivAlgHom [FiniteDimensional K L] :
     (L ≃ₐ[K] L) ≃* (L →ₐ[K] L) :=
   (Algebra.isAlgebraic_of_finite K L).algEquivEquivAlgHom K L
 #align alg_equiv_equiv_alg_hom algEquivEquivAlgHom
 
-end Algebra
+end Field
+
+end
 
 variable {R S : Type _} [CommRing R] [IsDomain R] [CommRing S]
 

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2019 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
-
-! This file was ported from Lean 3 source module ring_theory.algebraic
-! leanprover-community/mathlib commit 2196ab363eb097c008d4497125e0dde23fb36db2
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.FiniteDimensional
 import Mathlib.RingTheory.IntegralClosure
 import Mathlib.Data.Polynomial.IntegralNormalization
 
+#align_import ring_theory.algebraic from "leanprover-community/mathlib"@"2196ab363eb097c008d4497125e0dde23fb36db2"
+
 /-!
 # Algebraic elements and algebraic extensions
 

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

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

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

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

@@ -155,7 +155,7 @@ theorem isAlgebraic_algHom_of_isAlgebraic {B} [Ring B] [Algebra R B] (f : A →
 /-- Transfer `Algebra.IsAlgebraic` across an `AlgEquiv`. -/
 theorem AlgEquiv.isAlgebraic {B} [Ring B] [Algebra R B] (e : A ≃ₐ[R] B)
     (h : Algebra.IsAlgebraic R A) : Algebra.IsAlgebraic R B := fun b => by
-  convert← isAlgebraic_algHom_of_isAlgebraic e.toAlgHom (h _) ; refine e.apply_symm_apply ?_
+  convert← isAlgebraic_algHom_of_isAlgebraic e.toAlgHom (h _); refine e.apply_symm_apply ?_
 #align alg_equiv.is_algebraic AlgEquiv.isAlgebraic
 
 theorem AlgEquiv.isAlgebraic_iff {B} [Ring B] [Algebra R B] (e : A ≃ₐ[R] B) :

Changes are of the form

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

@@ -216,7 +216,7 @@ variable [Algebra R S] [Algebra S A] [Algebra R A] [IsScalarTower R S A]
 then A is algebraic over K. -/
 theorem isAlgebraic_trans (L_alg : IsAlgebraic K L) (A_alg : IsAlgebraic L A) :
     IsAlgebraic K A := by
-  simp only [IsAlgebraic, isAlgebraic_iff_isIntegral] at L_alg A_alg⊢
+  simp only [IsAlgebraic, isAlgebraic_iff_isIntegral] at L_alg A_alg ⊢
   exact isIntegral_trans L_alg A_alg
 #align algebra.is_algebraic_trans Algebra.isAlgebraic_trans
 

Part 3 of #5001

@@ -239,7 +239,7 @@ theorem isAlgebraic_of_larger_base_of_injective (hinj : Function.Injective (alge
   _root_.isAlgebraic_of_larger_base_of_injective hinj (A_alg x)
 #align algebra.is_algebraic_of_larger_base_of_injective Algebra.isAlgebraic_of_larger_base_of_injective
 
-/-- If x is a algebraic over K, then x is algebraic over L when L is an extension of K -/
+/-- If x is algebraic over K, then x is algebraic over L when L is an extension of K -/
 theorem _root_.isAlgebraic_of_larger_base {x : A} (A_alg : _root_.IsAlgebraic K x) :
     _root_.IsAlgebraic L x :=
   _root_.isAlgebraic_of_larger_base_of_injective (algebraMap K L).injective A_alg

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

@@ -308,7 +308,7 @@ variable {R S : Type _} [CommRing R] [IsDomain R] [CommRing S]
 
 theorem exists_integral_multiple [Algebra R S] {z : S} (hz : IsAlgebraic R z)
     (inj : ∀ x, algebraMap R S x = 0 → x = 0) :
-    ∃ (x : integralClosure R S)(y : _)(_ : y ≠ (0 : R)), z * algebraMap R S y = x := by
+    ∃ (x : integralClosure R S) (y : _) (_ : y ≠ (0 : R)), z * algebraMap R S y = x := by
   rcases hz with ⟨p, p_ne_zero, px⟩
   set a := p.leadingCoeff
   have a_ne_zero : a ≠ 0 := mt Polynomial.leadingCoeff_eq_zero.mp p_ne_zero
@@ -323,7 +323,7 @@ if `S` is the integral closure of `R` in an algebraic extension `L` of `R`. -/
 theorem IsIntegralClosure.exists_smul_eq_mul {L : Type _} [Field L] [Algebra R S] [Algebra S L]
     [Algebra R L] [IsScalarTower R S L] [IsIntegralClosure S R L] (h : Algebra.IsAlgebraic R L)
     (inj : Function.Injective (algebraMap R L)) (a : S) {b : S} (hb : b ≠ 0) :
-    ∃ (c : S)(d : _)(_ : d ≠ (0 : R)), d • a = b * c := by
+    ∃ (c : S) (d : _) (_ : d ≠ (0 : R)), d • a = b * c := by
   obtain ⟨c, d, d_ne, hx⟩ :=
     exists_integral_multiple (h (algebraMap _ L a / algebraMap _ L b))
       ((injective_iff_map_eq_zero _).mp inj)

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